Diffusion of Isotope Tracers in Binary Liquid Solutions

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

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

New fast organic scintillators using intramolecular bromine quenching

A new technique for measuring the Fickian diffusion coefficient in binary liquid solutions

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

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)

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.

We introduce the time-resolved phosphorescence anisotropy (TPA) method to study rotational diffusion of phosphorescent colloidal silica spheres in dispersions and in random close packings of host spheres. The tracer diffusion coefficients in sphere dispersions agree with hard-sphere predictions, demonstrating that TPA is a reliable technique for studying rotational dynamics. We also assess the rotational diffusion of phosphorescent tracers in sphere packings, exploiting the fact that the TPA technique can be used for slightly turbid samples. We find that the fraction of immobilized tracers directly reflects the pore size distribution as extracted from the Voronoi construction of a simulated random close packing. A calculation of the average distance between tracer and neighboring particle shows that the dependence of the rotational diffusion coefficient on the average distance between tracer and medium spheres is stronger for packings than for dispersions.

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.

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.

Femtosecond laser-induced optical kerr dynamics in CS 2/alkane binary solutions

On the correlation of macroscopic and microscopic rate constants in solid state chemistry

Self-diffusion and collective diffusion of hydrogen in TaH x