Ternary Diffusion Coefficients Research Articles

Ternary diffusion coefficients of monoethanolamine and N-methyldiethanolamine in aqueous solutions

Ternary diffusion coefficients of monoethanolamine (MEA) and N-methyldiethanolamine (MDEA) in aqueous solutions have been measured at 303.2, 313.2, and 323.2 K. The systems studied are aqueous solutions containing total amine concentrations of 2.5 and 4.0 kmol/m 3 and each solution prepared with four different amine molar ratios. The main diffusion coefficients ( D 11 and D 22) and cross-diffusion coefficients ( D 12 and D 21) and the density and viscosity of the aqueous amine solutions are discussed and analyzed as a function of temperature and their concentration.

Effect of Macromolecular Polydispersity on Diffusion Coefficients Measured by Rayleigh Interferometry

Rayleigh interferometry has been extensively used for the precise determination of diffusion coefficients for binary and ternary liquid mixtures. For ternary mixtures, the 2x2 matrix of multicomponent diffusion coefficients is obtained. Polydispersity adds complexity to the meaning of these measured diffusion coefficients. Here we discuss three important issues of polydispersity regarding the diffusion measurements extracted from this interferometric technique. First, we report novel equations for the extraction of diffusion moments from the Rayleigh interferometric pattern. These moments are used to define polydispersity parameters for macromolecular systems. We have experimentally determined mean diffusion coefficients and polydispersity parameters for aqueous solutions of poly(ethylene glycol) and poly(vinyl alcohol) at 25 degrees C. Aqueous solutions of poly(ethylene glycol) mixtures were used to examine the accuracy of the polydispersity parameters. Second, we compare Rayleigh interferometry to dynamic light scattering. Specifically, we have performed diffusion measurements on the same system using both techniques. To our knowledge, no direct experimental comparison between dynamic light scattering and classical methods for the measurements of diffusion coefficients has been previously reported in relation to polydispersity. We find that substantial discrepancies (i.e., 1 order of magnitude) between the mean diffusion coefficients obtained from these two different techniques can be observed when polydispersity is large. Third, for two-solute mixtures with one polydisperse solute, we report a novel corrective procedure for extracting accurate ternary diffusion coefficients from Rayleigh interferometry. Computer simulations were used to examine the accuracy of the extracted ternary diffusion coefficients.

A comparison of diffusion coefficients for ternary mixed micelle solutions measured by macroscopic gradient and dynamic light scattering techniques

Taylor dispersion is used to measure ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of decylsulfobetaine (SB10) (1) + dodecylsulfobetaine (SB12) (2), SB10 (1) + SB14 (2), and SB12 (1) + SB14 (2) mixed zwitterionic micelles. Cross-coefficient D(21) for the coupled flow of surfactant 1 produced by a concentration gradient in surfactant 2 is relatively small for these solutions, but D(12) reaches values as large as the main D(ii) coefficients. The results are interpreted by using the equation D(ik) = partial differential(C(i)D(i))/ partial differentialC(k) to relate the ternary mutual diffusion coefficients to the concentration-weighted average diffusion coefficients D(i) of the micellar and free-monomer forms of the surfactants. The macroscopic-gradient Taylor measurements are compared with diffusion coefficients measured by dynamic light scattering (DLS), which monitors microscopic concentration fluctuations. At most compositions, the intensity autocorrelation function G(tau) is a single exponential decay in D((2)), the smaller eigenvalue of the mutual diffusion coefficient matrix. A contribution from D((1)) is identified at high solute fractions of surfactant 1. The DLS results are consistent with contributions to G(tau) from uncoupled fluctuations in the concentrations of eigencomponents defined as the linear combinations of surfactants 1 and 2 that diagonalize the D(ik) matrix. A procedure for the rapid and convenient DLS measurement of ternary mutual diffusion coefficients, including the cross-coefficients for coupled diffusion, is suggested, using the Onsager reciprocal relation together with the eigenvalues and pre-exponential factors from G(tau).

Ternary Diffusion Coefficients of Monoethanolamine and Triethanolamine in Aqueous Solutions Containing Monoethanolamine and Triethanolamine

Ternary diffusion coefficients of monoethanolamine (MEA) and triethanolamine (TEA) in aqueous solutions containing MEA and TEA using the Taylor dispersion technique have been measured for temperatures 303.2, 308.2, and 313.2 K. The systems studied were aqueous solutions containing total amine concentrations of 2.0 and 3.0 kmol·m–3, each having three different amine-molar ratios. The density and viscosity of the blended amine solutions were also measured. The mutual diffusion coefficients of aqueous MEA and aqueous TEA solutions were also reported. The main diffusion coefficients (D11 and D22) and the cross diffusion coefficients (D12 and D21) were reported as function of temperature and concentration of alkanolamines. The limiting conditions for the main diffusion coefficients and the cross diffusion coefficients were discussed at first, and a comparison between the ratios of the cross diffusion coefficients to the main diffusion coefficients for MEA and TEA was made. Finally, the dependence of the main diffusion coefficient Dik on the viscosity of solutions was investigated.

Ternary Mutual Diffusion Coefficients of NH4Cl-(NH4)2SO4-H2O at 298.15 K by Optical Interferometry

Isothermal ternary diffusion coefficients measured by optical methods are reported at twelve sets of mean concentrations for the NH4Cl+(NH4)2SO4+H2O system at 298.15 K. Results are given for electrolyte solute concentration fractions of 0.25, 0.5, and 0.75 at total solute concentrations of 1, 2, 3, and 4 mol⋅dm−3. Also included are values of the densities, concentration derivatives of the densities, and the partial molar volumes. Results are compared with values for similar systems.

Multicomponent Diffusion of Lysozyme in Aqueous Calcium Chloride. The Role of Common-Ion Effects and Protein−Salt Preferential Interactions

To investigate the effect of calcium salts on the thermodynamic and transport properties of aqueous solutions of proteins, we report ternary diffusion coefficients for the lysozyme-CaCl2-water ternary system at 25 degrees C and pH 4.5. We have used our ternary diffusion coefficients to calculate preferential-interaction coefficients as a function of salt concentration. This has allowed us to characterize protein-salt thermodynamic interactions. We have observed the presence of large common-ion effects by examining the dependence of the diffusion coefficients on salt concentration. Our results are compared to those previously reported for the lysozyme-MgCl2-water ternary system. We have found that the common-ion effect is essentially the same for both salt cases. On the other hand, by examining the dependence of the preferential-interaction coefficient on salt concentration, we have found that salt preferentially interacts with the protein in the lysozyme-CaCl2-water system, whereas water preferentially interacts with the protein in lysozyme-MgCl2-water system. This is consistent with the known generally larger affinity of Mg2+ for water, as compared to Ca2+, and the different roles that these two divalent metal ions play in biochemical processes. We remark that neglecting the common-ion contribution of the preferential-interaction coefficient can lead to qualitatively inaccurate descriptions of protein-salt aqueous systems, even at high salt concentrations. Indeed, for the lysozyme-CaCl2 system, this approximation would lead to interpretations inconsistent with the known destabilizing effect of calcium ions on proteins.

Ternary Diffusion Coefficients of Glycerol + Acetone + Water by Taylor Dispersion Measurements at 298.15 K. 3. Water-Rich Region

Ternary Diffusion Coefficients of Glycerol + Acetone + Water by Taylor Dispersion Measurements at 298.15 K. 3. Water-Rich Region

Ternary Diffusion Coefficients of Glycerol + Acetone + Water by Taylor Dispersion Measurements at 298.15 K. 2. Acetone-Rich Region

The concentration dependence of the mutual diffusion coefficients in the ternary liquid mixture glycerol + acetone + water is determined at 298.15 K by the Taylor dispersion technique. As a continuation of previous measurements, we selected three concentration paths of a constant water mole fraction of x3 = 0.1, 0.2, and 0.3, respectively, ranging from the limit of the binary subsystem toward the phase boundary in the ternary system. The eigenvalues and the determinant of Fick's diffusion coefficient matrix are given.

Sorption and diffusion measurements in ternary polymer–solvent–solvent systems by means of a magnetic suspension balance—Experimental methods and correlations with a modified Flory–Huggins and free-volume theory

Diffusion and sorption data of methanol and toluene in the ternary system methanol–toluene–poly(vinylacetate) (pvac) were measured by means of a magnetic suspension balance (MSB). Ternary diffusion coefficients were determined from sorption kinetics with a method of Crank [1975. The Mathematics of Diffusion, second ed. Claredon Press, Oxford] classically used for binary polymer solvent systems. Assumptions and limitations for this method are discussed. Sorption data of methanol and toluene in the ternary system were correlated with a modified Flory–Huggins theory taking four instead of three interaction parameters into account and compared with predictions of UNIFAC-FV. All four binary Flory–Huggins interaction parameters were correlated as a function of concentration, determined from binary polymer–solvent sorption measurements and from solvent–solvent equilibrium data. The modified Flory–Huggins approach for ternary systems predicts the two limiting cases for the binary polymer–solvent as well the two solvent–solvent equilibria. Diffusion coefficients determined from sorption kinetics measurements were correlated with free-volume theory predictions of Vrentas et al. [1984. Self diffusion in polymer–solvent–solvent systems. Journal of Polymer Science, Polymer Physics Edition, 22, 459–469] and compared with a few available literature data from Surana et al. [1998. Diffusion and equilibrium measurements in ternary polymer–solvent–solvent systems using inverse gas chromatography. Industrial and Engineering Chemistry Research, 37, 3203–3207]. Cross diffusion terms are not taken into account. Diffusion and sorption data, determined with this gravimetric method, were used in model simulations with modified Flory–Huggins and free-volume theory to predict drying curves of ternary methanol–toluene–pvac solutions. The results were compared with previously published experimental results performed by means of Inverse-Micro-Raman-Spectroscopy (IMRS) from Schabel [2004. Trocknung von Polymerfilmen - Messung von Konzentrationsprofilen mit der Inversen-Mikro-Raman-Spektroskopie. Ph.D. Thesis, Universität Karlsruhe (TH), Germany].

The Effect of Salt Stoichiometry on Protein−Salt Interactions Determined by Ternary Diffusion in Aqueous Solutions

We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 degrees C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross-diffusion coefficients are very sensitive to salt stoichiometry. One of the cross-diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical-potential cross-derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.

Ternary diffusion coefficients—Theoretical treatment and application to theIn-situ-reinforced TiB2/Al composite

In the present work, a new model is developed to predict ternary diffusion coefficients in liquid state based on hard sphere theory and the Miedema model, and the diffusion coefficients are theoretically determined starting from the quantities of the pure component. Using this model, the diffusion coefficient of Ti in the TiB2/Al composite is evaluated and the influence of alloying element additions on the diffusion coefficient of Ti is discussed. The results indicate that additions of Si can promote the diffusion of Ti. Meanwhile, other elements including Cu, Fe, Mg, V, Ni, La, and Zr can hinder the diffusion of Ti. It is furthermore concluded that not only the phase diagram but also considerations concerning the kinetics are required to produce the desirable phases.

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W 1/2 of Taylor dispersion profiles using D=(ln 2)r 2 t R/(3W 2 h) and values of the retention time t R and dispersion tube radius r. The generalized expression D h=−(ln h)r 2 t R/(3W 2 h ) is derived to evaluate diffusion coefficients from peak widths W h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.

Ternary Diffusion Coefficients of 1-Hexanol-Hexane-Toluene and 1-Propanol-Water-Ethylene Glycol by Taylor Dispersion Method

The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients directly by fitting the mathematical solutions of the dispersion equation to eluted solute peaks detected using a differential refractometer. Diffusion coefficients of the three-component system of acetone-benzene-CCl 4, determined at 25°C, were used to test the procedure. The measured diffusion coefficients were compared with values obtained by optical interferometry and the diaphragm cell method. Ternary diffusion coefficients are also determinated for solutions of 1-hexanol-hexane-toluene and 1-propanol-water-ethylene glycol at 25°C, with an accuracy of approximately 0.05 m 2·s −1.

Ternary Diffusion Coefficients of Glycerol + Acetone + Water by Taylor Dispersion Measurements at 298.15 K

The concentration dependence of the mutual diffusion coefficients in the ternary liquid mixture glycerol + acetone + water is determined at 298.15 K by the Taylor dispersion technique along two concentration paths of constant water mole fractions of 0.468 and 0.420, ranging from the binary subsystem toward the phase boundary in the vicinity of the critical solution point. The eigenvalues of Fick's diffusion coefficient matrix are given, and the influence of the optical properties of the system on the diffusion coefficient determination is discussed. It was found that the determinant |D| continuously declines on approaching the phase boundary.

Estimation of Diffusion Coefficients in Bitumen Solvent Mixtures as Derived From Low Field NMR Spectra

Abstract Use of solvents for the extraction of heavy oil and bitumen appears to be an increasingly feasible technology. Both vapour extraction and direct solvent injection are considered for conventional exploration and production schemes, while solvent dilution of bitumen is a standard technique in oil sands mining. Mass transfer between solvent and bitumen is a poorly understood process. In some cases, it is totally ignored compared to viscous force effects. In other cases, phenomenological estimations of diffusion and dispersion coefficients are used. Low field NMR has been used successfully in determining both solvent content and viscosity reduction in heavy oil and bitumen mixtures with various solvents. As a solvent comes into contact with a heavy oil or bitumen sample, the mobility of hydrogen bearing molecules of both solvent and oil changes. These changes are detectable through changes in the NMR relaxation characteristics of both solvent and oil. Relaxation changes can then be correlated to mass flux and concentration changes. Based on Fick's Second Law, a diffusion coefficient, which is independent of concentration, was calculated against three oils and six solvents. Introduction There are extensive deposits of heavy oil and bitumen in Alberta. These fields are primary candidates for thermal and solvent based processes for recovery of oil and bitumen. Both vapour extraction and direct solvent injection are considered for in situ exploration and production schemes, while solvent dilution of bitumen is a standard technique in oil sands extraction as part of the secondary froth flotation. Mass transfer between solvent and bitumen is a poorly understood process. Only a few experimental values of the diffusion coefficient of various organic substances into bitumen are available in the open literature(1 –4). To better understand oil/solvent mass transfer phenomena, more experimental data are necessary, especially in liquid-liquid systems. In this paper, such experimental data are obtained for three oils and six solvents. Most methods for studying mass transfer between two liquids employ some type of an optical system to record time dependent patterns that can be photographed and then analyzed to yield either the binary or the ternary diffusion coefficients for the system of interest(5). The work presented in this paper is a deviation from such methods. In the presented work, low field Nuclear Magnetic Resonance (NMR) was used as the tool for mixing pattern recording. Low field NMR has great potential as a tool for measuring properties of reservoir fluids and produced liquid streams(6). From a single NMR measurement of a fluid stream containing oil and water, the relative fractions of both liquids can be determined(7). Low field NMR has been used successfully in determining both solvent content and viscosity reduction in heavy oil and bitumen mixtures with various solvents(8, 9). As a solvent comes into contact with a heavy oil or bitumen sample, the mobility of hydrogen bearing molecules of both solvent and oil change. These changes can be correlated to mass flux and concentration changes. If Fick's Second Law of diffusion is used to model such mass flux and consequent concentration changes, then an apparent diffusion coefficient can be calculated.

Comparison of ternary diffusion coefficients obtained from dynamic light scattering and Taylor dispersion

Over the last decade dynamic light scattering (DLS) has developed into a powerful technique for the determination of transport properties in liquids and liquid mixtures. Its advantague is based on the fact that microscopic fluctuations in concentration and temperature are used to characterize the transport behavior and no external macroscopic gradients are needed. All classical methods of Fick's diffusion coefficient determination, like Taylor dispersion (TD) or interferometric methods, however, use macroscopic concentration gradients and give a diffusion coefficient matrix.In the present paper we report results of diffusion coefficient measurements in ternary liquid mixtures of glycerol(0)–acetone(1)–water(2) at 298.15K. Taylor dispersion technique is used to determine the mutual diffusion coefficients Dij along a path of constant mole fraction of water x2=0.4200 from the binary edge towards the critical solution point in the ternary mixture. These results are compared with dynamic light scattering data in the vicinity of the critical solution point and along the very same path of constant x2. The aim of the comparison is to identify the physical character of the mass diffusion mode Dm obtained in our previous DLS measurements. We found that in this ternary system the diffusion mode Dm is not related to any of the diffusion coefficients Dij but we can clearly show that it coincides with the lowest eigenvalue of Fick's diffusion coefficient matrix. There are theoretical arguments which, at least in the vicinity of the critical solution point, lead to the conjection that this behavior might be general for ternary systems with molecules of similar size.

An electrostatic mechanism for the coupled diffusion of polymer molecules and ionic micelles. Aqueous poly(ethylene glycol) + sodium dodecyl sulfate solutions

Taylor dispersion is used to measure ternary mutual diffusion coefficients for aqueous PEG200 [poly(ethylene glycol), average molecular weight 200 g mol−1] + NaDS (sodium dodecyl sulfate) and PEG3400 + NaDS solutions at 25 °C. Diffusion coefficients are reported for solutions containing 1 or 3 wt% PEG and NaDS at concentrations from 0.0035 to 0.25 mol dm−3. The PEG200 and NaDS fluxes are weakly coupled, but PEG3400 concentration gradients can drive substantial coupled fluxes of NaDS (up to 17 mol NaDS per mol of PEG3400 driven by its own gradient), an order of magnitude larger than the coupled fluxes predicted by thermodynamic and excluded-volume theories of coupled diffusion. An electrostatic mechanism is proposed to account for the strong interactions between PEG and NaDS fluxes based on the association of PEG molecules and NaDS micelles, which reduces the charge density on the micelles and releases bound Na+ counterions. The diffusion of relatively mobile free Na+ ions down PEG concentration gradients generates an electric field which pulls along a coupled flux of the oppositely-charged NaDS micelles to maintain electroneutrality. The measured coupled fluxes of NaDS are in qualitative agreement with predictions made using Nernst–Planck equations and increases in free Na+ ion activity with added PEG measured with a sodium ion-selective electrode.

Mathematical model for diffusion of a protein and a precipitant about a growing protein crystal in microgravity.

Equations are presented that model diffusion of a protein to the surface of a growing crystal in a convection-free environment. The equations apply to crystal growth solutions that contain both a protein and a protein precipitant. The solutions are assumed ternary and the equations include all four diffusion coefficients necessary for the full description of the diffusion process. The four diffusion coefficients are assumed constant. Effects of crystal/solution moving boundary and the effect of a protein adsorption barrier at the crystal interface are included. The equations were applied to the system lysozyme chloride + NaCl + H2O, which has served as the primary model system for the study of crystal growth of proteins and for which there are now published ternary diffusion coefficients. Calculated results with and without the inclusion of cross-term diffusion coefficients are compared.

Incongruent Diffusion (Negative Main Mutual Diffusion Coefficient) for a Ternary Mixed Surfactant System

Moments analysis of Taylor dispersion profiles is used to measure ternary mutual diffusion coefficients (Dik) for dilute aqueous sodium dodecyl sulfate (SDS) + dodecylsulfobetaine (DSB) mixed surfactant solutions at 25 °C and total surfactant concentrations from 10 to 30 mmol dm-3. The fluxes of the SDS(1) and DSB(2) components are strongly coupled by the formation of SDS−DSB mixed micelles. At several compositions, cross-coefficient D12 or D21 is larger than main coefficients D11 and D22. More remarkably, D22 is negative at solute fractions of SDS from 0.55 to 0.75, reaching a minimum value of −0.056 × 10-9 m2 s-1 at 13 mmol dm-3 SDS + 7 mmol dm-3 DSB. This surprising result means that DSB concentration gradients drive “incongruent” fluxes of DSB, from lower to higher DSB concentrations. A possible explanation for the incongruent diffusion of DSB is suggested on the basis of the electric field generated by gradients in the surfactant concentration. Negative Dii values have been reported previously for concentrated, strongly nonideal aqueous acetic acid + chloroform solutions near a consolute point. Because the SDS + DSB solutions are dilute and far removed from phase boundaries, incongruent diffusion might be considerably more common than previously assumed.

Relating multicomponent mutual diffusion and intradiffusion for associating solutes. Application to coupled diffusion in water-in-oil microemulsions

The binary mutual diffusion coefficient (D) for a dilute solution of a self-associating solute and the solute intradiffusion coefficient (D*) are related by D = D* + (dD*/dC), where C is the total solute concentration. This relation is extended to multicomponent systems. For solutions of two associating solutes, the ternary mutual diffusion coefficients D11, D12, D21, D22 and the solute intradiffusion coefficients D*1, D*2 are found to be related by D11 = D1* + C1∂D*1/∂C1, D12 = C1∂D*1/∂C2, D21 = C2∂D*2/∂C1, and D22 = D2* + C2∂D*2/∂C2. These results are used to interpret coupled diffusion in water + AOT (sodium bis(2-ethylhexyl)sulfosuccinate) + n-heptane (water-in-oil) microemulsions. Although the water(1) and AOT(2) components associate and intradiffuse together through the heptane–continuous solvent as AOT-coated water droplets, and hence D*1 ≈ D*2, the mutual diffusion of AOT is more rapid than that of water (D22 > D11), and there are counter-current coupled flows of AOT (D21 < 0) and large co-current coupled flows of water (D12 > 0). This behavior can be understood by noting that added water reduces the Brownian motion of the droplets by swelling the water cores (∂D*i/∂C1 < 0), whereas added AOT reduces the droplet size (∂D*i/∂C2 > 0) by providing more surfactant to coat the water. The predicted water and AOT intradiffusion coefficients are the eigenvalues of the mutual diffusion coefficient matrix.