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

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

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.

Measurements of mutual diffusion coefficients of several metal chlorides in aqueous solutions close to infinite dilution have been made with the Taylor dispersion technique. Data were obtained for alkaline earth metal chlorides. BeCl2/H2O, MgCl2/H2O, CaCl2/H2O, SrCl2/H2O, and BaCl2/H2O, and for third-family metal chlorides, AlCl2/H2O, and GaCl3/H2O. All the measurements were obtained at five temperatures between 298.15 and 318.15 K. A linear dependence between the mutual diffusion coefficient and temperature was found. In the range of temperatures studied here, the values of the mutual diffusion coefficients follow a sequence: BaCl2 > SrCl2 > CaCl2 > MgCl2 > BeCl2 for alkaline-earth metal chlorides and GaCl3 > AlCl3, for third-family metal chlorides. That is, the higher the atomic weight of the cation. the higher the mutual diffusion coefficient. A comparison of mutual diffusion coefficients of alkaline, alkaline earth, and third-family metal chlorides is presented.

We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz along the direction of advection. It is characterized by the kinetic coefficients—the advection velocity, diffusion coefficient and the reaction kernel, quantifying the aggregation rates. We analyze a simplified model with mass-independent advection velocity, diffusion coefficient, and reaction rates. We also examine a model with mass-dependent coefficients arising in the context of aggregation with sedimentation. For the quasi-stationary case and simplified model, we obtain an exact solution for the spatially dependent agglomerate densities. For the case of mass-dependent coefficients we report a new conservation law and develop a scaling theory for the densities. For the numerical efficiency we exploit the low-rank approximation technique; this dramatically increases the computational speed and allows simulations of very large systems. The numerical results are in excellent agreement with the predictions of our theory.

Transport properties in aqueous ethambutol dihydrochloride

The inverse gas chromatography (IGC) method has been evaluated as a method to determine diffusion coefficients in polymer–solvent systems near the glass transition temperature. The poly(vinyl acetate)–toluene system was used for this purpose. Diffusion and partition coefficients were measured over a wide range of temperature. At temperatures significantly above the glass transition of the polymer, the capillary column model developed by Pawlisch and co-workers1,2 was used. At temperatures near the glass transition temperature, the modification of the capillary column model, proposed by Vrentas et al.3 was used. A sensitivity analysis of the capillary column model was made to delineate the range of applicability of the model. The diffusion coefficients obtained from IGC were compared with those extrapolated from the gravimetric sorption technique. The values agree within the expected range of error. Finally, free-volume theory was evaluated for its ability to predict the temperature and concentration dependencies of diffusion coefficients at temperatures near the glass transition from high temperature IGC data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1233–1240, 1997

We report light scattering measurements of the static structure factor and mutual diffusion coefficient for the compatible polymer mixture poly (phenylmethylsiloxane)/poly(styrene). The measurements were made for a series of molecular weights of the poly(styrene) of 2000, 4000, and 9000 for different volume fractions of the poly(styrene) over a range of temperatures from 350 to 520 K. The principal aim was to try and distinguish between the various theoretical approaches which have appeared in the literature and which give radically different results for the concentration dependence of the mutual diffusion coefficient in a binary polymer mixture. Since the static structure factor was measured in the same light scattering experiment as the diffusion coefficient we have also been able to obtain the concentration, molecular weight, and temperature dependence of the Onsager coefficient directly from experiment. A concentration-dependent glass transition temperature complicates the comparison with theory and we propose a method for the data analysis to deal with this problem. Our results are consistent with the expression for diffusion coefficient based on the dynamic random phase approximation.

ABSTRACTKinetic properties of γ-phase (Cu5Zn8) growth in the binary system Cu-Zn were studied at 160-270°C. It has been found that γ-phase grows in diffusional-kinetic regime. Both kinetic coefficients of interfacial reaction rate β and diffusion coefficients D have been determined taking into account Kirkendall effect. Arrhenius equations for the kinetic and diffusion coefficients have been obtained, with the high values of “dynamic” diffusion coefficients and low activation energies for both diffusion (QD) and interfacial reaction (Qβ). The mechanism of Zn diffusion in non-stoichiometric Cu5Zn8 phase is discussed.

The effects of ionic strength and pH on the diffusion coefficients and gross conformation of chitosan molecules in solution were studied. Chitosan with 83% degree of deacetylation (DD) was prepared from red shrimp (Solemocera prominenitis) processing waste. Ten different molecular weight chitosans were prepared by ultrasonic degradation, and their molecular weights were determined by static light scattering. The weight-average molecular weight (Mw) were between 78 to 914 kilo dalton (KDa). Solution of different ionic strengths (I = 0.01, 0.10, and 0.20) but the same pH (2.18) and different pHs (2.37, 3.10, and 4.14) but the same ionic strength (I = 0.05) were prepared to measure their mutual diffusion coefficient (Dm). The diffusion coefficients for standard condition (D20,w) were derived from Dm. Intrinsic viscosities ([η]) were determined by a capillary viscometer in different pH solutions. The Mark–Houwink exponents a and ε were obtained from plots of Log [η] and Log D20,w versus Log Mw, respectively. The results show that diffusion coefficients increased with increasing ionic strength or with increasing pH or with decreasing Mw. Value of ε and a were between 0.503 to 0.571 and ranged from 0.543 to 0.632, respectively. The results indicates that chitosans conformation were in random coil in solutions in the ranges of ionic strength and pH studied. The values of a*, ε* and a**, ε**, Mark–Houwink exponents of smaller and higher than 223 KDa chitosans, respectively, were between 0.752 to 0.988 and 0.585 to 0.777 for smaller Mw chitosans and 0.406 to 0.428 and 0.430 to 0.518 for larger Mw chitosans, respectively. Molecular-weight-induced conformational transition occurred because smaller Mw chitosans was more extended than higher Mw chitosans. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2041–2050, 1999

Analysis of the mutual diffusion coefficient of hyaluronate reveals that it rapidly increases with increasing concentration or decreasing ionic strength. The mutual diffusion coefficients analyzed by boundary relaxation in the analytical ultracentrifuge by either Raleigh interference optics or absorption optics (through the use of fluorescein‐labeled hyaluronate) yielded similar values. The theoretical treatment of the mutual diffusion coefficient has been analyzed in terms of experimentally measured intradiffusion coefficients and thermodynamic virial coefficients. Only approximate agreement between theory and experiment was found. The concept of formation of transient statistical network structures in semidilute solutions of hyaluronate was applied to evaluate a critical concentration at which network formation occurs. This has been discussed in relation to the marked decrease in the intradiffusion coefficient of hyaluronate with concentration. The formation of network structures in hyaluronate was found not to preclude the hyaluronate undergoing extremely rapid rates of mutual diffusion (with diffusion coefficients ∼30 × 10−11 m2 s1) under conditions of relatively large initial chemical potential gradients. Measurements of the unidirectional flux of hyaluronate for nonzero gradients demonstrated their marked sensitivity to the magnitude of the concentration difference across the boundary. An experimental feature of the unidrectional diffusion coefficients of hyaluronate is that they may be analyzed purely in terms of mutual and intradiffusion processes. The backflux diffusion coefficient (describing the flux against the imposed concentration gradient) appeared identical with the intradiffusion coefficient. The analysis of the various sources of errors made in this study suggests that the magnitude of the diffusion coefficients measured may be regarded only as approximate.

Measurements are reported for the scattering of argon beams with energies between about 200–1500 eV by room-temperature argon, helium, and hydrogen. Two separate investigations in essentially the same apparatus are involved, and interaction potentials are derived for Ar–Ar and Ar–He at internuclear distances where scattering measurements have not previously been made. For Ar–H2 there are no previous direct scattering results. The Ar–Ar system was studied in both investigations, and the combined results are represented by V(r) = 3.25 × 103 / r9.97eV, 1.96 Å < r < 2.41 Å. There is good agreement between this result and potentials from other scattering measurements and shock compression of liquid argon. One series of new measurements was made for Ar–He. The derived potential is V(r) = 22.2 / r5.42eV, 1.40 Å < r < 1.81 Å, which agrees well with other scattering results and with measurements of mutual diffusion coefficients at elevated temperatures. A combination of He–He potentials obtained from scattering with the present Ar–Ar results leads to a derived He–Ar potential which is in good agreement with that obtained from the direct measurements. One series of measurements was made for Ar–H2, and the resulting potential is V(r) = 159 / r6.28eV, 1.81 Å < r < 2.36 Å, which is about a factor of 2 higher than that derived from previous measurements on He–He, He–H2, and Ar–Ar. It is also higher by about the same amount than the Ar–H2 potential derived from other scattering measurements on Ar–Ar and H2–H2. Mutual diffusion coefficients for Ar–H2 at elevated temperatures also suggest that this potential is high. The present potential for Ar–Ar agrees well with theoretical calculations based on a delta-function model and a statistical (Thomas–Fermi–Dirac) model. The Ar–He potential also agrees with calculated potentials based on these models and with that obtained from ab initio Hartree–Fock calculations.

The mutual diffusion coefficients for polybutadiene‐ethylbenzene and polybutadiene‐n‐nonane systems were measured by using a sorption apparatus with a quartz spring in the temperature region from 80 to 130°C and for mass fraction of hydrocarbon ranging from 0 to 0.27. The mutual diffusion coefficients were correlated with good agreement by the free‐volume theory.

The mutual (or collective) diffusion coefficient of Brownian particles treated in most of previous microscopic theories is regarded as defined on the basis of the dynamic structure factor. It is pointed out for cases where both direct and hydrodynamic pair interactions are present between Brownian particles that this diffusion coefficient does not satisfy the generalized Einstein relation which results from conventional irreversible thermodynamics and which should be obeyed by the diffusion coefficient as would be determined by conventional gradient diffusion experiments. This is ascribed to the fact that the diffusion coefficient based on the dynamic structure factor is generally not identical with the conventional diffusion coefficient, i.e., whereas the latter diffusion coefficient describes the collective diffusion of Brownian particles under conditions of uniform temperature and pressure, the former describes that under conditions of uniform temperature and uniform chemical potential of solvent. A correct expression for the conventional diffusion coefficient is derived by taking this difference into account. Both diffusion coefficients are evaluated for the case of hard spheres.

Anomalies in the concentration fluctuations and the mutual diffusion coefficient of 2-dimensional Lennard–Jones mixture in the supercritical region