John G. Albright

Ternary mutual diffusion coefficients and densities of the system {z1NaCl +(1 –z1)Na2SO4}(aq) at 298.15 K and a total molarity of 0.5000 mol dm–3

Isothermal ternary mutual diffusion coefficients (interdiffusion coefficients) have been measured for the system {z1NaCl +(1 –z1)Na2SO4}(aq) at a constant total molarity of 0.5000 mol dm–3 and 298.15 K using either Rayleigh or Gouy interferometry. Measurements were performed at NaCl molarity fractions of z1= 1, 0.90, 0.75, 0.50, 0.25 and 0. Densities of all solutions used in the diffusion experiments were measured using pycnometers and/or a vibrating densimeter. Trace diffusion coefficients have been evaluated from these results for the Cl–(aq) ion in 0.5 mol dm–3 Na2SO4(aq) and for the SO42–(aq) ion in 0.5 mol dm–3 NaCl(aq). The resulting values are D*(Cl–)=(1.681 ± 0.002)× 10–9 m2 s–1 and D*(SO42–)=(0.900 ± 0.006)× 10–9 m2 s–1, respectively. At all compositions, (D21)v, the cross-term diffusion coefficient of Na2SO4 due to a concentration gradient of NaCl, was found to be negative, whereas (D12)v, the cross-term diffusion coefficient of NaCl due to a concentration gradient of Na2SO4, was found to be positive.

Effects of different sized concentration differences across free diffusion boundaries and comparison of Gouy and Rrayleigh diffusion measurements using NaCl−KCl−H2O

Diffusion was systematically studied in the ternary system NaCl (0.5M)−KCl (0.5M)−H2O at 25°C. There were four purposes. First, current methods to extractDij from Gouy and Rayleigh interferometry data depend on treating theDij as effectively constant. If concentration differences ΔCi across the boundary are large, this may not be true. To explore this issue, four sets of experiments were performed. Each set had four experiments with approximately the same total number of fringesJ. Each set also had the same corresponding ΔC1/ΔC2 ratios as the other three, but the ΔCi were adjusted such that the four sets hadJ≈30, 60, 90, and 120, respectively. Noclear dependence of theDij on ΔCi was found within their realistic errors. Second, the Gosting diffusiometer can yield both Rayleigh and Gouy fringe patterns during the same experiment. Therefore, theDij from both methods were compared, and agree well. Third, a new method for analyzing Gouy fringe positions (Miller; program TNY) can be compared to the classical one (Fujita-Gosting; program RFG). TheDij from both analyses agree well. Fourth, we compared results from the Gosting diffusiometer with those at the same composition from other diffusiometers: one data set by O[Donnell and Gosting from an older Gouy apparatus, and three Rayleigh sets at differentJ values from our older Model H diffusiometer. Results from older diffusiometers were more scattered, but correspondingDij agree within realistic errors. As reported previously, realistic errors are approximately four times the statistical errors obtained by least squares. Recommended Rayleigh and GouyDij are presented for this composition.

Measurement of mutual diffusion coefficients, densities, viscosities, and osmotic coefficients for the system KSCN-H2O at 25°C

Mutual diffusion coefficients measured on the volume-fixed frame of reference are reported for KSCN-H2O at 25°C over the concentration range 0.0 to 10.26 mol-dm−3. The diffusion coefficient at infinite dilution was obtained from limiting ionic equivalent conductances of K+ and SCN−. Low concentration conductances of KSCN-H2O at 25°C used to obtain the limiting ionic equivalent conductance of SCN− are reported. Values of density and viscosity for this system are reported from 0.0 to 10.30 mol-dm−3. Osmotic coefficienss of KSCN-H2O at 25°C were measured by the isopiestic method. These are reported over the concentration range of 0.30 to 24.94 molal (saturation). Values of thermodynamic diffusion coefficients for the concentration range 0.0 to 10.26 mol-dm−3 are tabulated. Results are compared to other potassium salts with monovalent anions at 25°C.

Quaternary Diffusion Coefficients in a Protein-Polymer-Salt-Water System Determined by Rayleigh Interferometry

We have experimentally investigated multicomponent diffusion in a protein-polymer-salt-water quaternary system. Specifically, we have measured the nine multicomponent diffusion coefficients, D(ij), for the lysozyme-poly(ethylene glycol)-NaCl-water system at pH 4.5 and 25 degrees C using precision Rayleigh interferometry. Lysozyme is a model protein for protein-crystallization and enzymology studies. We find that the protein diffusion coefficient, D(11), decreases as polymer concentration increases at a given salt concentration. This behavior can be quantitatively related to the corresponding increase in fluid viscosity only at low polymer concentration. However, at high polymer concentration (250 g/L), protein diffusion is enhanced compared to the corresponding viscosity prediction. We also find that a protein concentration gradient induces salt diffusion from high to low protein concentration. This effect increases in the presence of poly(ethylene glycol). Finally, we have evaluated systematic errors associated with measurements of protein diffusion coefficients by dynamic light scattering. This work overall helps characterize protein diffusion in crowded environments and may provide guidance for further theoretical developments in the field of protein crystallization and protein diffusion in such crowded systems, such as the cytoplasm of living cells.

Determination of Preferential Interaction Parameters by Multicomponent Diffusion. Applications to Poly(ethylene glycol)-Salt-Water Ternary Mixtures

Poly(ethylene glycol) (PEG) is a hydrophilic nonionic polymer used in many biochemical and pharmaceutical applications. We report the four diffusion coefficients for the PEG-KCl-water ternary system at 25 degrees C using precision Rayleigh interferometry. Here, the molecular weight of PEG is 20 kg mol(-1), which is comparable to that of proteins. The four diffusion coefficients are examined and used to determine thermodynamic preferential interaction coefficients. We find that the PEG preferential hydration in the presence of KCl is 1 order of magnitude larger than that previously obtained under the same conditions for lysozyme, a protein of similar molecular weight. In correspondence, the coupled diffusion in the PEG case was greater than that observed in the lysozyme case. We attribute this difference to the greater exposure of polymer coils to the surrounding fluid compared to that of globular compact proteins. Moreover, we observe that the PEG preferential hydration significantly decreases as salt concentration increases and attribute this behavior to the polymer collapse. Finally, we have also employed the equilibrium isopiestic method to validate the accuracy of the preferential interaction coefficients extracted from the diffusion coefficients. This experimental comparison represents an important contribution to the relation between diffusion and equilibrium thermodynamics.

The mutual diffusion study in the systems containing benzene or benzene‐d6 at 25 °

The mutual diffusion coefficients of benzene and benzene‐d6 were measured at low solute concentrations in each of the following solvents: n‐hexane, cyclohexane, dodecane, and hexadecane. The observed mutual diffusion coefficients for the systems containing benzene‐d6 were consistently lower than those observed for the corresponding systems containing benzene. The results of this investigation show that a measurable isotope effect exists in liquid diffusion and that the magnitude of the effect depends on the physiochemical properties of the solvents. The magnitude appears to be more closely related to the viscosity of the solvents than to the molecular weights of the solvents.

Measurement of mutual-diffusion coefficients for the system KNO3-H2O at 25°C

Mutual-diffusion coefficients measured on the volume fixed frame of reference are reported for KNO3−H2O at 25°C over the concentration range 0.025 to 2.61M. The diffusion coefficients decrease monotonically from 1.928×10−9 m2-sec−1 to 1.166×10−9 m2-sec−1 as the concentration increases from 0.0 to 2.61M. A series of density measurements are reported for this system over the molar concentration range of 0.082 to 2.513M.

Methods for the analysis of ternary free-diffusion processes by the Rayleigh optical interferometric method

Equations are presented for the analysis of ternary free-diffusion processes in liquid systems by the Rayleigh optical interferometric method. Four different analytical derivations are given and two numerical methods of analysis are discussed.

Protein Diffusiophoresis and Salt Osmotic Diffusion in Aqueous Solutions

Diffusion of a solute can be induced by the concentration gradient of another solute in solution. This transport mechanism is known as cross-diffusion. We have investigated cross-diffusion in a ternary protein-salt-water system. Specifically, we measured the two cross-diffusion coefficients for the lysozyme-NaCl-water system at 25 °C and pH 4.5 as a function of protein and salt concentrations by Rayleigh interferometry. One cross-diffusion coefficient characterizes salt osmotic diffusion induced by a protein concentration gradient, and is related to protein-salt thermodynamic interactions as described by the theories of Donnan membrane equilibrium and protein preferential hydration. The other cross-diffusion coefficient characterizes protein diffusiophoresis induced by a salt concentration gradient, and is described as the difference between a preferential-interaction coefficient and a transport parameter. We first relate our experimental results to the protein net charge and the thermodynamic excess of water near the protein surface. We then extract the Stefan-Maxwell diffusion coefficient describing protein-salt interactions in water. We find that the value of this coefficient is negative, contrary to the friction interpretation of Stefan-Maxwell equations. This result is explained by considering protein hydration. Finally, protein diffusiophoresis is quantitatively examined by considering electrophoretic and hydration effects on protein migration and utilized to accurately estimate lysozyme electrophoretic mobility. To our knowledge, this is the first time that protein diffusiophoresis has been experimentally characterized and a protein-salt Stefan-Maxwell diffusion coefficient reported. This work represents a significant contribution for understanding and modeling the effect of concentration gradients in protein-salt aqueous systems relevant to diffusion-based mass-transfer technologies and transport in living systems.

Diffusion studies of bile acids, fatty acids and sucrose-NaCl-water systems at 37 °C by a modified capillary cell apparatus and their application to membrane transport studies

Abstract A capillary cell apparatus is described that allows accurate measurement of solute tracer diffusion coefficients in biological solutions at 37 °C. The apparatus has a unique stirring mechanism to provide a uniform flow pattern over the capillaries with only 18 ml of the bulk solution. Four capillaries of 2 cm length are used. With this apparatus measurement can be made at relatively short time periods so that bacterial overgrowth in the solutions is minimized. Using this apparatus tracer diffusion coefficients of three bile acids, cholic, taurochollic and taurodeoxycholic acids, and four fatty acids, acetic, pentanoic, octanoic and decanoic acids, were measured in an isotonic phosphate buffer, pH 7.1, at 37 °C. Viscosity, density and diffusion coefficients of sucrose in physiological saline solutions were also measured.