Prediction of the mutual diffusivity in binary liquid mixtures containing one dimerising species, from the tracer diffusion coefficients

Prediction of the mutual diffusivity in binary non-ideal liquid mixtures from the tracer diffusion coefficients

Light scattering measurement and theoretical interpretation of mutual diffusion coefficients in binary liquid mixtures

A study was made of miscible polymer blends of deuterated polystyrene (d‐PS) and tetramethylbisphenol‐A polycarbonate (TMPC). The Flory interaction parameter χ was obtained from the relation between mutual and tracer diffusion coefficients, D̃ and D*, which were measured by forward recoil spectrometry. The temperature dependence of diffusion at PS weight fractions ω of 0.25 and 0.5, and the composition dependence at temperatures 45°C above the glass transition temperature, Tg, were investigated. A stronger dependence of χ on both temperature (at ω = 0.5) and composition was observed in comparison with other miscible binary polymer blends involving PS. Analysis using the generalized lattice‐fluid model of Sanchez and Balazs1 showed that the incorporation of a significant specific interaction is needed to explain the temperature dependence of χ. The diffusion coefficients obtained in the one‐phase region were extrapolated to the two‐phase region, and these were compared with the effective diffusion coefficient extracted from phase separation dynamics measured by light scattering.2 A significant discrepancy between the extrapolated and effective diffusion coefficients was observed. © 1995 John Wiley & Sons, Inc.

The tracer diffusion coefficient of radioactive benzene in mixtures of benzene and rubber at 25° C has been measured over the whole range of composition. Variation of diffusion coefficient with composition can be described by a formula of the Fujita type. Results have been combined with published values of the mutual diffusion coefficient and the thermodynamic properties. They are interpreted in terms of a “one-process” theory and show that mobility of benzene molecules in mutual diffusion at low concentrations of rubber is greater than that in tracer diffusion by a factor which rises to 4.2 when the concentration of rubber is 5%. Results are incompatible with the “two-process” theory of diffusion, unless this theory is modified by inclusion of an adjustable parameter.

The behaviour of isotope tracers in diffusion processes was investigated. In systems of organic binary solutions gradients of chemical concentration were present. Using the capillary method the tracer and the mutual diffusion coefficients were determined. It was found that the tracer diffusion coefficient is equal to the mutual one if the tracer moves in the same directions as the unlabelled part of component and the ratio of both parts of component is time independent. When both conditions are not justified the tracer diffusion is due to the simultaneously mutual and self‐diffusion processes.

Photon correlation spectroscopy (PCS) has been used to measure the mutual diffusion coefficient Dm for unliganded hemoglobin in the concentration range 0.86 to 15.7 g/dl. The result corrected to water at 20 °C is Dm=Do[1−(0.0057±.0003)c] where Do= (6.75±0.05) ×10−7 cm2/s and c is in units of g/dl. It is shown that Dm can be used with the phenomenological theory of diffusion to predict the tracer diffusion coefficient Dt and that the predictions agree with the results of diaphragm cell measurements [Keller, et al., J. Phys. Chem., 75, 379 (1971)]. In contrast to this, diaphragm cell measurements of Dm do not agree with PCS measurements, with open capillary and free diffusion experiments [Kitchen, et al., J. Polymer Sci. Sym. No. 55, 39 (1976)], or with ultrafiltration measurements [Probstein, et al., J. Phys. Chem. 83, 1228 (1979)]. The evidence indicates that Dm≠Dt for hemoglobin, and that diaphragm cell measurements of Dm are not reliable for proteins. (AIP)

Tracer diffusion coefficients D* of lithium ions in LixMn2O4 (0.2 < x < 1) thin films were measured as a function of the composition x by using secondary ion mass spectrometry. For this purpose, a new “step-isotope-exchange method” was developed to observe the time dependence of the 6Li isotope concentration ratio in the LixMn2O4 film which is in contact with a 6Li-enriched electrolyte to exchange Li+ ions. A steep decrease in D* depending on the Li composition was observed for LixMn2O4, with D* = 8 × 10–13 cm2 s–1 for x = 0.2 and decreasing to 1.5 × 10–17 cm2 s–1 for x = 1.0 (bulk diffusion coefficient, Db*). This behavior is well explained by a vacancy diffusion model for the α phase on LixMn2O4 (0.77 < x < 1.0). Chemical diffusion coefficients D̃ were also measured in the range of 0.2 < x < 1.0 by an electrochemical method, which was compared with the D* to evaluate the effect of thermodynamic factors. The thermodynamic factors and interactions between Li+ ions were found to strongly influence the chemical diffusion coefficient. The tracer diffusion measurements are important to understand the charge–discharge mechanism in the electrodes of lithium-ion batteries.

Dependence of diffusion coefficients characterizing mutual diffusion and selfdiffusion of oligomeric tracers on the composition of equilibrium swollen polymer hydrogels was studied. The hydrogels were characterized by their dynamic correlation lengths ξ measured by DLS and by concentrations of elastically active network chains ν determined by measurement of their elastic moduli. Diffusion coefficients of macroscopic translational diffusion of paramagnetic tracers (poly(ethylene glycol)s spinlabeled with nitroxides) in gels were measured by electron spin resonance imaging (ESRI) [1], self-diffusion and mutual diffusion coefficients of corresponding diamagnetic tracers (poly(ethylene glycol)s without nitroxides) were measured by pulsed-gradient stimulated NMR spin-echo (PGSTE) and dynamic light scattering (DLS), respectively. 2. Experimental Hydrogels A, B, C, and D equilibrium-swollen with water were prepared by lightinduced copolymerization of 2-hydroxyethyl methacrylate (HEMA) with 2-(2-hydroxyethoxy)ethyl methacrylate (DEGMA) using 2,3-dihydroxybutane-1,4-diyl dimethacrylate as crosslinker and 2-hydroxy-2-methyl-1-phenylpropan-1-one as initiator. Compositions of batches leading to equilibrium-swollen hydrogels given in the Table were selected in preliminary experiments. Copolymerization was performed in sealed sample tubes the diameter of which was designed to meet demands of particular experiments: thin glass capillary of o.d. ≈ 1 mm for ESRI, glass sample tube of o.d. 4 mm for PGSTE NMR and glass sample tube of o.d. 10 mm for DLS, gravimetry and measurement of elastic moduli. Possible differences between the water contents in the batch and equilibrium water contents in the hydrogels were checked gravimetrically in long-term swelling experiments. ESRI experiment was started by topping the hydrogel in the glass capillary (o.d. ≈ 1 mm, gel cylinder length 3 - 5 mm) with a drop of aqueous solution of the tracer (0.2 μL, 10 -2 mol/L), the capillary was resealed and placed in the spectrometer cavity with the cylinder axis oriented vertically, parallel to the direction of the magnetic field gradient. Shapes of concentration profiles of the paramagnetic tracer inside the sample along the magnetic field gradient, approaching equilibrium distribution due to the tracer diffusion, were measured by ESRI [2] at suitable times after the diffusion start. Diffusion coefficients of the paramagnetic tracers were found by analysis of the time dependence of the tracer concentration profiles, based on the solution of Fick’s equation appropriate for the sample geometry [3]. Diffusion coefficients of the diamagnetic

One of the Darken equationsgives a relationship between the intrinsic and the tracer diffusion coefficients, D_{A} and D_{A}^{*}, of species A in a solid binary mixture. In its original formulation, the equationreads D_{A}=D_{A}^{*}Γ, with Γ the thermodynamic factor. The question addressed in this paper is how D_{A} and D_{A}^{*} depend separately on Γ. Using a recent result for transition probabilities in terms of the excess chemical potential [M. Di Muro and M. Hoyuelos, Phys. Rev. E 104, 044104 (2021)2470-004510.1103/PhysRevE.104.044104], it is shown that the intrinsic diffusivity does not depend on Γ. This approach simplifies a previous theoretical analysis that reaches the same result. Experimental results of diffusion in Ni-Pd and Fe-Pd alloys [M. J. H. van Dal et al., Acta Mater. 48, 385 (2000)1359-645410.1016/S1359-6454(99)00375-4] are used to check the theory. Numerical simulations of Ni-Pd were performed to show that the migration energy is the main factor responsible for the increase in diffusivity at intermediate concentrations.

Within the framework of an international benchmark test we have performed measurements of the transport coefficients S T (Soret coefficient), D (mutual diffusion coefficient) and D T (thermal diffusion coefficient) on the three binary organic liquid mixtures 1,2,3,4-tetrahydronaphthalene- n -dodecane, 1,2,3,4-tetra- hydronaphthalene-isobutylbenzene and isobutylbenzene- n -dodecane with the weight fraction c = 0.5 at T = 298.15 K by means of thermal-diffusion-forced Rayleigh scattering (TDFRS) for benchmarking purposes. Our results for the coefficients are in good agreement with those obtained by annular and parallelepipedic thermogravitational columns and by other benchmark tests which also apply TDFRS measurements.

Molecular weight dependence of the tracer diffusion coefficient of short chains in the microphase domain of block copolymers as studied by the pulsed-field gradient nuclear magnetic resonance method

A simple and absolute closed capillary method is introduced for measuring tracer diffusion coefficients in liquids with both γ- and β-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.

Composition dependence of tracer diffusion coefficients in Fe–Ga alloys: A case study by a tracer-diffusion couple method

Augmentation of Oxygen Transport by Various Hemoglobins as Determined by Pulsed Field Gradient NMR

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.