Integral Diffusion Coefficient Research Articles

Atomic diffusion in liquid gallium and gallium-nickel alloys probed by quasielastic neutron scattering and molecular dynamic simulations

The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-based ab-initio molecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K. Machine learning force fields derived from ab-initio molecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficient DGa(T) follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However, DGa(T) can be well described alternatively by an Einstein–Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.

Recyclability of poly(hydroxybutyrate-co-hydroxyhexanoate) (PHBH) for food packaging applications

This study is the first to investigate the recyclability of poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBH), a small chain length PHA, and evaluate the gas barrier properties of the recycled materials. A recycling simulation of PHBH was performed through five twin-screw extrusion cycles. Although the onset degradation temperature and the chemical structure of the processed PHBH remained stable, size exclusion chromatography and melt flow index revealed a drop of 24.3% in the molar mass of the recycled materials. However, the recycled samples showed higher impact strength and, therefore, are less brittle and more elastic. Gas barrier properties of PHBH were found to enhance after the first recycling step. A significant decrease in both permeability and diffusion coefficients was observed after the first extrusion cycle. At the same time, the calculated mean integral diffusion coefficient <D> as well as the plasticization factor (γCeq) demonstrate a weak water plasticization effect for recycled materials.

Modelling boron diffusion for Fe2B layer formation: comparative kinetics analysis in pack-boronized AISI 4147 steel

Abstract In this current research paper, the modelling of boron diffusion during the powder-pack boronizing was achieved by utilizing two kinetics approaches: the integral method and average diffusion coefficient (ADC) method. This integral method used a general solution of algebraic differential equations (DAEs) system. The powders mixture composed of: 33.5 wt% B4C, 5.4 wt% KBF4 and 61.1 wt% SiC was employed to generate the Fe2B layers on AISI 4147 steel in the interval of 1123–1273 K for 2–8 h. The obtained surface layers have been characterized by Scanning electron microscopy (SEM) to examine the growth front with a typical saw-toothed morphology. The crystalline nature of boride phase has been verified by X-ray diffraction technique (XRD). The calculation results arising from the two models led to the similar boron activation energy in Fe2B equal to 196.19 kJ mol−1. Additionally, both models were checked out empirically by selecting three extra boronizing conditions obtained at 1273 K for increasing times (2.5, 4.5 and 8.5 h). The predicted layers’ thicknesses were found to be in line with the experimental results.

Phase competition in ternary Ti–Ni–Al system

In this paper the reactive diffusion in Ti–Ni–Al system is discussed at 1173 K. The calculation method based on the binary approach is presented. The key kinetic parameter is Wagner integral diffusion coefficient. The experimental and simulation results of reactive diffusion between pure Ti and β-NiAl are compared at 1173 K after 100 h.

The Impact of Microstructure Geometry on the Mass Transport in Artificial Pores: A Numerical Approach

The microstructure of porous materials used in heterogeneous catalysis determines the mass transport inside networks, which may vary over many length scales. The theoretical prediction of mass transport phenomena in porous materials, however, is incomplete and is still not completely understood. Therefore, experimental data for every specific porous system is needed. One possible experimental technique for characterizing the mass transport in such pore networks is pulse experiments. The general evaluation of experimental outcomes of these techniques follows the solution of Fick’s second law where an integral and effective diffusion coefficient is recognized. However, a detailed local understanding of diffusion and sorption processes remains a challenge. As there is lack of proved models covering different length scales, existing classical concepts need to be evaluated with respect to their ability to reflect local geometries on the nanometer level. In this study, DSMC (Direct Simulation Monte Carlo) models were used to investigate the impact of pore microstructures on the diffusion behaviour of gases. It can be understood as a virtual pulse experiment within a single pore or a combination of different pore geometries.

Phase transformations in iron-nitride compound layers upon low-temperature annealing: Diffusion kinetics of nitrogen in ▓- and γ′-iron nitrides

The ▓/γ′-iron nitride (▓-Fe3N1+x, γ′-Fe4N) compound double layers with thicknesses of about 10 µm were grown on pure α-Fe, by gas nitriding at 823 K, followed by quenching. The specimens were subsequently annealed at significantly lower temperatures, in the range of 613 to 693 K, for different periods of time. These heat treatments led to a redistribution of N, within the compound layer as well as between the compound layer and the adjacent ferrite, inducing thickness changes in the ▓-and γ′-sublayers. The microstructure and sublayer-thickness changes were analyzed by light microscopy and X-ray diffraction (XRD). The experimentally observed time and temperature dependences of the layer-thickness changes were compared with the results obtained from numerical simulations, by adopting a model based on volume diffusion in the ▓- and γ′-phases and on local equilibrium at the phase interfaces. In this manner, the intrinsic diffusion coefficient of N in the ▓-phase and the integral diffusion coefficient of N in the γ′-phase were determined for the applied range of annealing temperatures.

Method for the measurement of the diffusion coefficient of benzalkonium chloride

Biofilm formation on the optical ports of cameras and underwater sensors is the primary cause of their reduced useful deployment time. The use of a transparent hydrogel coating containing the cationic surfactant benzalkonium chloride has been shown to extend the deployment times for up to 12 weeks for these instruments. In order to predict the effective lifetime of these coatings it was necessary to obtain the diffusion coefficient of the benzalkonium chloride used in the coatings. Benzalkonium chloride can have different alkyl chain lengths ranging from C8H17 to C18H37 with chain length greatly affecting its chemical properties. The benzalkonium chloride materials investigated here were mixtures of C12H25 and C14H29 as well as C14H29 on its own. These materials were selected for their proven biofilm resistant qualities. The diaphragm diffusion cell technique was investigated for its applicability to the measurement of diffusion coefficients of molecules with surfactant properties and the ability to form micelles. The method was found to be satisfactory for the cationic surfactant benzalkonium chloride. The average value of the membrane cell integral diffusion coefficient D̄ was 7.78×10−6cm2s−1 at 25°C and there was no significant effect of alkyl chain length on the measured value of D̄.

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part IV. D( C)/ D0=1+( αC)− β( αC) 2

Using the specific functional form D( C)/ D 0=1+( αC)− β( αC) 2 an investigation has been made of (isothermal) transport through a slab membrane under ‘simple’ boundary conditions and governed by a diffusion coefficient, D( C), which, with increasing concentration, at first increases, passes through a maximum value and finally decreases. The flux, integral diffusion coefficient and concentration profile characteristic of steady-state permeation have been evaluated; special attention has been paid to the positions of such profiles in relation to the corresponding linear distribution associated with a constant diffusion coefficient. The corresponding transient-state transport has been studied within a framework of the time-lag ‘early-time’ and ‘ t ’ procedures. Expressions for the ‘adsorption’ and ‘desorption’ time-lags are given. The concentration-dependence of these time-lags, of the (four) integral diffusion coefficients derived from them and of the arithmetic-mean time-lag ratios have been considered in some detail. The ‘early-time’ and ‘ t ’ finite-difference procedures have likewise been employed to derive four further integral diffusion coefficients, so enabling a comparison to be made of the nine integral coefficients pertaining to established experimental techniques. Particular interest attaches to the situation for which n≡ β( αC 0)=1 (where C 0 is the ingoing or upstream concentration of diffusant) resulting in D( C 0) being symmetrical about C 0/2. Some consideration has been given, in general, to features of transient-state transport when governed by a symmetrical D( C).

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: III. Numerical solution of the diffusion equation: ‘early-time’ and ‘ [formula omitted]’ procedures

Using the method of finite differences, numerical solution of the diffusion equation for a slab membrane has been effected for five functional dependencies of the (differential) diffusion coefficient upon concentration. Transient-state concentration profiles corresponding with ‘adsorption’ and ‘desorption’ permeation have been employed to derive fluxes and quantities of diffusant crossing a plane perpendicular to the flow. The ‘adsorption’ and ‘desorption’ fluxes J a( l, t) and J d(0, t), were then used to construct ‘early-time’ plots from the slopes of which integral diffusion coefficients D ̃ 1 a and D ̄ 1 d were derived. Similarly, from the amounts of diffusant crossing the ingoing and outgoing faces of the membrane, Q a(0, t) and Q d( l, t), ‘ t ’ plots were constructed, the slopes of which yielded a further pair of integral diffusion coefficients: D ̄ 3 a and D ̃ 3 d . For each system studied a comparison of nine integral diffusion coefficients has been made. Those derived from the slope of the ‘early-time’ plots gave the two ends of the integral diffusion coefficient ‘spectrum’, the remaining seven coefficients lying between these limits. For both the strictly-increasing and strictly-decreasing functions employed it was observed that D ̃ 1 a ≅D 0 , D ̄ 1 d ≅D(C 0) . Some consideration has been given to ‘weighted-mean’ (integral) diffusion coefficients.

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part II. The four time-lags for some particular D( C)

Expressions have been derived for the ‘adsorption’ ( L l a( C 0), L 0 a( C 0)) and ‘desorption’ ( L 0 d( C 0), L l d( C 0)) time-lags corresponding with 13 functional dependencies of the differential diffusion coefficient, D( C). A detailed analysis of the concentration dependence of the time-lags is given. The initial ( C 0 → 0) slope and curvature of a time-lag : (ingoing) concentration curve may be obtained from the corresponding limiting values of d D( C 0)/d C 0 and d 2 D( C 0)/d C 0 2. It is shown how the ‘desorption’ time-lags and ingoing ‘adsorption’ time-lag are related to the (experimentally) more readily determined outgoing ‘adsorption’ time-lag, L l a( C 0) and may be evaluated using a master-plot of steady-state flux of diffusant, J ∞( C 0), against ingoing concentration, C 0. The arithmetic mean of designated time-lag integral diffusion coefficients can, over a limited range of C 0, approximate to the steady-state integral diffusion coefficient D̃( C 0). This finding, combined with determination of the complementary J ∞( C 0) should allow an estimate of C 0 to be made. Following upon experimental observations, attention has been directed towards the concentration dependence of ‘adsorption’ and ‘desorption’ time-lag ratios, R a ( C 0) and R d( C 0) and of the arithmetic mean, R M( C 0) = (1/2)[ R a( C 0) + R d( C 0)]. Departures of R M( αC 0) from the ideal value of 2 were not great and were hardly reflected in the corresponding larger variations of R a( C 0) and R d( C 0).

A Simple Method for Determining Differential Diffusion Coefficients from Aqueous Electrolyte Diaphragm Cell Data at Temperatures Below 0°C

A method is introduced to allow the calculation of differential diffusion coefficients from integral diffusion coefficient data collected with diaphragm cells below 0°C. The method is demonstrated with concentrated potassium hydroxide diaphragm cell data at −15°C and with published data from Stokes. Differential diffusion coefficients, calculated using Stokes' method and the proposed method, are compared for the HCl‐water system at 25°C. © 1999 The Electrochemical Society. All rights reserved.

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient. Part I. The four time-lags: some general considerations

Two (equivalent) sets of expressions have been derived for the four time-lags, L a l , L d 0, L d l , L a 0, associated with transport through a slab membrane under `simple' boundary conditions and with the diffusion coefficient, D, a function of the concentration, C, of the diffusing species. The individual sign and relative magnitudes of the time-lags have been determined. Order of magnitude has been derived for two particular classes of D( C): Class (A): D( C) a strictly-increasing function of C and Class (B): D( C) a strictly-decreasing function of C, thereby establishing the two time-lag sequences: ( A) L a 0<L d l<0<L d 0<L a l, ( B) L d l<L a 0<0<L a l<L d 0. The four time-lags have been employed to define four integral diffusion coefficients: D ̃ a L, D d L, D ̃ d L, D a L. Inequalities between these (time-lag) integral diffusion coefficients and the corresponding steady-state integral diffusion coefficient, D̃, have been investigated. For the particular Classes (A) and (B) functions considered, the sequences of time-lag moduli are: ( A) 2L d 0<|L d l|<|L a 0|<2L a l, ( B) 2L d 0>|L d l|>|L a 0|>2L a l.

Methods of Measuring Diffusion Coefficients of Water and Potassium Chloride in Aqueous Solution in Cellulose Acetate Membranes

Abstract An open-ended capillary cell has been developed to measure thermodynamic diffusion coefficients of electrolytes, in aqueous solution, in swelled polymeric membranes. Also a new method to determine the integral diffusion coefficient of water in membranes is presented. In this work we present a description of the methods as well as the experimental results of the diffusion coefficients of potassium chloride and water in cellulose acetate (CA) membranes. The results are in good agreement with those described elsewhere which shows the reability of the methods.

Separation of Volatile Organic Compounds by Pervaporation for a Binary Compound Combination: Trichloroethylene and 1,1,1-Trichloroethane

This study evaluates the behavior of sweeping air pervaporation when used to separate trichloroethylene (TCE) and 1,1,1-trichloroethane (TCEthane) from wastewater. Selectivity and membrane preference are studied. Models for binary compounds are studied to evaluate the extent of cross influence on TCE flux due to the presence of another volatile organic compound, TCEthane. Using the models, the integral dry diffusion coefficient for TCEthane is evaluated. Results indicate that the membrane exhibits a preference for TCE over TCEthane. However, the values of the diffusion rates are found to be comparable. Selectivity values are found to be independent of the air flow rate but dependent on the relative concentration of the compounds in the feed solution. It is found that, due to the presence of TCEthane, the flux of TCE decreased. Further, it is found that the ratio of the integral dry diffusion coefficients of the compounds is inversely proportional to the ratio of their molecular weights.

Sorption and transport of water vapor in alginic acid, sodium alginate, and alginate‐cobalt complex films

AbstractThe sorption and the transport of water vapor in films of alginic acid (G1), sodium alginate (G1Na), and alginate‐cobalt complex (G1Co) were studied at 30°C by employing the weighing method. Sorption isotherms for all films of G1, G1Na, G1Co were of type II in the Brunauer's classification. The integral absorption from, and desorption to, zero pressure were non‐Fickian type for all films studied. The mean permeability coefficient P, which was determined by the cup method, increased with the increase of vapor pressure, especially in the low vapor pressure region. P for G1Na was much higher than that for G1, which mainly reflects more hygroscopic nature of G1Na than that of G1. The values of P for G1Co were lower than those for G1 at lower pressures and then approached those for G1 at higher vapor pressures. Integral diffusion coefficient D evaluated as P/S, where the solubility coefficient S was evaluated from sorption isotherms, increased rapidly with increasing water concentration and then leveled off. In the concentration region studied, the magnitude of D and its dependence on concentration for H2O‐G1Na system did not differ much from those for H2O‐G1 system. D for H2O‐G1Co system was much lower than that for H2O‐G1 system. © 1994 John Wiley &amp; Sons, Inc.

Numerical examination of the dual‐mode model for permeation, sorption, and desorption rate curves

AbstractNumerical solutions were applied to the dual‐mode sorption and transport model for gas permeation, sorption, and desorption rate curves allowing for mobility of the Langmuir component. Satisfactory agreement is obtained between integral diffusion coefficient from sorption and desorption rate curves and apparent diffusion coefficient from permeation rate curves (time lag method). These rate curves were also compared to the curves predicted by Fickian‐type diffusion equations. © 1992 John Wiley &amp; Sons, Inc.

Diffusion and solution of methanol vapor in poly(2-vinylpyridine)- block- polyisoprene and poly(2-vinylpyridine)-block-polystyrene

Diffusion and solution behavior of methanol vapor in two diblock copolymers, poly(2-vinylpyridine)—block—polyisoprene [P(2VPbI)] and poly(2-vinylpyridine)—block—polystyrene [P(2VPbS)], was studied by the weighing method at 25°C. The domain structure of films of both copolymers showed an alternating lamellar arrangement. Methanol is a good solvent for P2VP, but a nonsolvent for PI and PS. Methanol dissolved exclusively in the P2VP phase of the copolymers. For both copolymer systems, absorption and desorption processes of non-Fickian type were observed as characterized by a thickness anomaly. However, the magnitude of the deviations from purely Fickian behavior was small, and the integral diffusion coefficient, D̄, was obtainable with reasonable accuracy. At low and medium concentrations, D̄ for P(2VPbI) was greater, by about one order of magnitude, than that for P2VP, while D̄ for P(2VPbS) was lower than that for P2VP. A similar trend was observed in plots of the permeability coefficient against the vapor pressure of methanol. The results indicate that the rubbery PI phase may facilitate the transport of penetrant molecules in the P(2VPbI) film. On the other hand, the glassy PS phase in the P(2VPbS) film merely interferes with the transport of methanol molecules.

Permeation characteristics of organic vapors in silicone rubber tubing

Since silicone rubber exhibits sufficient inertness, it can be used as a permeation device to generate known standard atmospheres of organic vapors. The permeation characteristics of organic vapors through silicone permeation tubes are examined by their transport phenomena under saturation steady state conditions. The permeation rate is a function of solubility and diffusion rate. The solubilities of organic vapors in silicone rubber can be estimated by the Flory-Huggins relationship with a single value of the interactive parameter (χ). The integral diffusion coefficient and the activation energy can be deduced from experimental permeation rate data and estimated solubility data. Several industrial organic vapors are studied at various concentrations, temperatures, and tube-wall thicknesses. The high permeation rate of organic vapors through silicone rubber is a consequence of the low energy for permeation.

Relationship between Integral Diffusion Coefficient and Rate Constant in Dyeing Polyethylene terephthalate) Fibres with Disperse Dyes

Practical methods of computing the diffusion coefficient D and rate constant Kfrom the Cegarra–Puente equation for dyeing poly (ethylene terephthalate) fibre with disperse dyes are given. A simple approximate relationship has been derived enabling the corresponding D to be found when K is known. A general technique is also described for approximation of complicated diffusion equations by means of simpler relationships.

202 - External transverse magnetic field effect on electrolyte diffusion in LiCl-H 2O solutions

Experiments using modified fritted glass diaphragm-cell method show that an externally applied magnetic field of 5 kG strength decreases (up to 0.7 %) the integral diffusion coefficient of LiCl (measured at 25 °C and at ambient pressure) in 0.04, 0.08, 0.4, 0.8 and 1.6 N LiClH 2O solution.