Diffusion Coefficient Dm Research Articles

Diffusion on a flexible surface

The self-diffusion of a particle on a flexible surface, such as a fluid bilayer membrane or a macroscopic interface, is analyzed theoretically in order to relate the macroscopic diffusion coefficient DM, describing displacements in a laboratory-fixed plane, to the intrinsic surface diffusion coefficient DS and to the configurational statistics of the surface. An exact result for DM is obtained for a rapidly fluctuating surface. For a static surface, rigorous bounds on DM are established and an effective medium approximation is derived that should remain accurate for strongly disordered surfaces. With the aid of these results, classical self-diffusion measurements can be used to study the configuration, bending rigidity, and interactions of flexible membranes and interfaces.

Solvent and Solute Effects on Hydration and Aggregation Numbers of Triton X-100 Micelles

Quasi-elastic light scattering spectroscopy was used to measure the mutual diffusion coefficient Dm of Triton X-100 micelles, and the probe diffusion coefficient Dp of polystyrene latex spheres diffusing through micelle solutions. The solution ionic strength has a substantial effect on aggregation number N and hydration δ of Triton X-100 micelles, N and δ both increasing with increasing salt concentration. This behavior may be qualitatively described as arising from a salt-induced change in the location of the water/Triton X-100 cloud curve.

Mutual diffusion in aqueous gel solutions

AbstractConcentration relations for mutual diffusion coefficients Dm(C) in water of polyelectrolyte gelatin macromolecules at different temperatures were studied by optical interferometry. It is shown that Dm(C) values are in agreement with scaling predictions and are similar to those observed for solutions of neutral macromolecules under θ‐conditions. However, they are greatly influenced by the square‐law term C2, having a correlation to the conventional scaling law Dm ∝︁ C, and the mobility of solution components is influenced by physical gelation processes under certain thermodynamic conditions. It is demonstrated that the temperature relation of the diffusion coefficient at infinite dilution D0(C → 0) for the three gelating samples with various physico‐chemical properties can be described by a universal function.

Dynamic light scattering from a semiflexible polymer at very low concentrations

Dynamic light scattering measurements on semiflexible poly(γ-benzyl-α,L-glutamate) have been performed at very low concentrations, near the limit for reliable multiangle detection, in N,N-dimethylformamide. By several methods of data analysis, the mutual diffusion coefficient Dm is initially level or slightly decreasing with polymer concentration. It then increases substantially, as expected in a good solvent. Static light scattering measurements offer no thermodynamic explanation for the initially level or decreasing behavior, which is apparently a manifestation of the decrease in lateral mobility as the rods become entangled in semidilute solutions. The coefficient C describing the dependence of the first cumulant of the electric field autocorrelation function upon squared scattering vector decreases with concentration, even in the most dilute regime measured. The reliability of persistence lengths estimated for this polymer by dynamic light scattering is considered.

Na+ and Cl− transport across polyimide films

AbstractNa+ and Cl‐ transport across 2.4‐ and 5.2‐μm‐thick polyimide (PI) PMDA/ODA and 7.5‐μm‐thick du Pont Kapton films was studied in a diffusion cell using ion‐selective electrodes. The temperature was 30°C. Diffusion coefficients Dm (in cm2/s), permeability coefficients P (in cm2/s), and distribution coefficients K were obtained by applying the time lag analysis on the ion uptake transient in the acceptor compartment of the diffusion cell. Both Na+ and Cl‐ were observed to diffuse across PI. Diffusion coefficients varied in the range 10‐12‐10‐13 cm2/s whereas ionic permeability results showed more scatter ranging from 1 X 10‐11 to 8 X 10‐14 cm2/s. The latter discrepancy was ascribed to diffuse heterogeneities on the order of 0.5 μm. No significant ionic selectivity between Na+ and Cl‐ was observed. This result indicates the absence of ionic fixed charge (unreacted polyamic acid) in the polymeric matrix. An attempt is made to determine the effect of water sorption mode and contaminants in the film on the ionic permeabilities data.

DETERMINATION OF DIFFUSION COEFFICIENT AND QUENCHING RATE COEFFICIENT OF METASTABLE N2 MOLECULES N2(A3∑u+) USING TOWNSEND DISCHARGING

The diffusion coefficient Dm and quenching rate coefficient Kq of metastable nitrogen molecule N2(A3∑u+) in pure N2 has been determined using Townsend dischaging. The values of Dm of 128 cm2/s and KN2 of 8.1×10-19 cm3/s were obtained respectively.

Diffusion of Strontium and Chloride in Compacted Clay‐based Materials

AbstractThis study examines the effect of pore solution composition and temperature on the measured and calculated diffusion coefficients (Dm and Dc, respectively) for Sr2+ in a compacted mixture of bentonite (50 wt%) and sand. Dm for Sr2+ and Cl‐ in the soil was determined at a dry bulk density of ∼1.7 Mg m−3 using deionized water (DW) and two synthetic groundwater solutions (SGW) with ionic strengths of 0.27 and 1.4 mol L−1 to saturate the soil, and at 25, 60, and 90°C. The Dc for Sr2+ was calculated from Dc = Doτ/(1 + ρbKd/θv), where Do is the diffusion coefficient of Sr2+ in free solution; τ is a tortuosity factor, obtained for the compacted soil from Cl‐ diffusion experiments; ρb is the dry bulk density; θv is the volumetric moisture content; and Kd is a distribution coefficient that accounts for the interaction of Sr2+ with the soil. Both Dm and Dc for Sr2+ increased with an increase in the ionic strength of the saturating solutions and with an increase in temperature. The Dm values were, however, always greater than Dc values by a factor of 6.2 to 8.0 for DW and 1.3 to 1.8 for the SGW with an ionic strength of 1.4 mol L−1. This difference is believed to be the result of obtaining Kd values in solutions that differed significantly from the pore solution of the compacted soil. Nevertheless, the results indicate that Dc values, which are often more convenient and less time‐consuming to obtain than Dm values, can at least be used to establish relationships and trends between the diffusion rates of some contaminants in clay‐based materials and the properties of these materials.

Diffusion of TiO2 probe particles through a poly(ethylene oxide) melt

AbstractQuasi‐elastic light scattering (QELS) spectroscopy was for the first time used to measure the mutual diffusion coefficient Dm of titanium dioxide (TiO2) particles of 0,37 μm and 0,31 μm diameters in a poly(ethylene oxide) melt (weight‐average mol. wt. 7 500) between 85 °C and 160 °C. Dm exhibits a strong dependence on the temperature. The effective shear imposed by diffusing particles on the polymer melt was estimated through a comparison of the viscosity obtained by a cone‐and‐plate viscometer with the microviscosity calculated from the diffusion coefficients and hydrodynamic radii of the particles through the Stokes‐Einstein equation. The rate of shear found was ≥ 104 · s−1.

Diffusion in concentrated micellar and hard sphere solutions

We present experimental results of quasi-elastic light scattering for different charged micellar solutions. The characteristic concentration dependence of the mutual diffusion coefficient Dm at large volume fraction arises from the many-body hydrodynamic interactions. These interactions are introduced through the quasi-empirical screened Navier-Stokes equation. The effective pair mobility tensor has been calculated for terms up to r -7 (r is the inter-particle distance) with the formalism of Mazur and van Saarloos. The tensor is not « screened » in the sense that its long distance behaviour is as an inverse power of r, rather than exponential. A single « screening » constant K is proposed which is volume fraction dependent with only one adjustable parameter. The evolution of Dm with the micellar concentration has been well reproduced by the same value of K at various ionic strengths. At large volume fraction Φ the hydrodynamic interactions are essentially dominated by uncharged hard-sphere repulsions. This observation is confirmed by the fit of the dynamics of concentrated hard-sphere solutions. The behaviour of the self and mutual diffusion coefficients is described by using the same « screening » constant. This can be written as Ka ≃ Φ where a is the particle radius, which is in agreement with the results previously derived by Adelman.

Photon and fluorescence correlation spectroscopy and light scattering of eye-lens proteins at moderate concentrations

The bovine eye-lens protein, alpha L-crystallin, has been studied with photon correlation spectroscopy to obtain the mutual diffusion coefficient, Dm, with fluorescence correlation spectroscopy to determine the tracer diffusion coefficient, DT, and with light scattering to get the isothermal osmotic compressibility (delta pi/delta c) P,T. The concentration dependence of Dm, DT, and (delta pi/delta c) P,T up to a volume fraction phi of the protein of 2.5 x 10(-2) has been interpreted on the basis of four different interaction potentials: (a) an extended hard-sphere potential; (b) a shielded Coulomb potential; (c) a shielded Coulomb interaction where the effect of counterions is included; (d) a simple mixed potential. The three parameters Dm, DT, and (delta pi/delta c) P,T have also been combined in the generalized Stokes-Einstein equation, Dm = [(delta pi/delta c)P,T . (1--phi) . (DT)]/(kappa B . T). Our results indicate that, in the case that photon correlation spectroscopy gives the mutual diffusion coefficient Dm, the applicability of the Stokes-Einstein equation can be questioned; or that, when one assumes the Stokes-Einstein equation to be valid, there is significant discrepancy between the result of photon correlation spectroscopy and Dm.

The second order concentration corrections to the mutual diffusion coefficient of Brownian macroparticles

From the initial time dependence of the dynamic structure factor S(k,t), we obtain a general form, valid through second order in the concentration, for the mutual diffusion coefficient Dm. All effects of direct and hydrodynamic interactions (other than dynamic friction) are taken into account, including the three-point ’’0seen’’ hydrodynamic tensor Tijl, whose analytic form is obtained here for the first time. The concept of the reference frame correction is re-examined. The usual factor (1−φ) for transition from the fundamental hydrodynamic frame to the volume-fixed frame is argued to be a low-concentration approximation. The general form for Dm is evaluated for a model system of hard spheres. With the use of the auxiliary assumption (relaxed herein) that all hydrodynamic interaction tensors satisfy ∇ ⋅ t = 0, use of our new general method [J. Stat. Phys. 28, 673 (1982)] for reducing N-particle cluster integrals to (N−1)-dimensional integrals shows Dm = D0 (1−0.875φ−19.53φ2).

Copolyester studies. VII. The dyeing behavior of undrawn fibers derived from tetramethylene terephthalate: Poly(tetramethylene oxide) random block copolymers

AbstractA series of copolymers based on poly(tetramethylene terephthalate) containing poly(tetramethylene oxide) blocks whose molecular weights ranged from 1000 to 5000 in concentrations from 10 to 30% by weight was prepared. The polymers were melt spun into fibers and the undrawn fibers dyed with a disperse dye at three temperatures. The equibrium adsorption and diffusion coefficient of the dye increased with both the molecular weight and concentration of the polyether. The equilibrium adsorption varied linearly with both the molecular weight and concentration. It has been assumed that the equilibrium dye partition coefficient KM gives a parameter of the accessibility, V, of the fiber for dye. If the diffusion coefficient DM is given by DM = VDo/τ, where Do is the diffusion coefficient of the dye in the amorphous regions and τ is a tortuosity factor, a good correlation can be obtained between KM and DM, suggesting that changes in Do/τ vary in a systematic fashion.

The wave vector dependence of diffusion coefficients in photon correlation spectroscopy of protein solutions

The mutual diffusion coefficient Dm was measured by means of photon correlation spectroscopy (PCS) for bovine serum albumin (BSA) at pH 4.7 and ionic strength I≃0.12 M. The BSA concentrations ranged from 1.00 to 10.7 g/dℓ and the magnitude of the scattering wave vector K varied from 3.21×104 to 3.51×105 cm−1. It was found that Dm=D0[1−(0.0166±0.0009)C], where D0=(5.92±0.04)×10−7 cm2/s corrected to water at 20 °C and the C measured in units of g/dℓ. The quantity Cn/K3, where Cn is the concentration in number of solute particles per cm3, ranged from 2 to 27 000, but this had no influence on the measured values of Dm. This work does not support the idea that the small size of K−1 or the small number of molecules contained in the volume K−3 affects the magnitudes of diffusion coefficients determined by PCS for proteins at moderate ionic strengths.

Contribution of nonhydrodynamic interactions to the concentration dependence of the friction factor of the mutual diffusion coefficient

The mutual diffusion coefficient Dm of a Brownian particle may be expressed as the ratio of a thermodynamic factor K and a friction factor fm, K and fm both being dependent on the macroparticle concentration. The contribution to fm of direct (e.g., hard sphere, electrostatic) interactions is here estimated to first order in the macroparticle concentration. In contrast to our earlier calculation [J. Chem. Phys. 67, 4690 (1977)] in which the direct interaction contribution Δfm to the Stokes’ Law drag coefficient was obtained from a fluctuation–dissipation equation. Δfm is here obtained directly from a mechanical argument based on the equations of motion of the macroparticles in solution. ΔfD is explicitly evaluated for the case of particles which interact through a weak Gaussian potential.

The nonelectrolyte permeability of planar lipid bilayer membranes.

The permeability of lecithin bilayer membranes to nonelectrolytes is in reasonable agreement with Overton's rule. The is, Pd alpha DKhc, where/Pd is the permeability coefficient of a solute through the bilayer, Khc is its hydrocarbon:water partition coefficient, and D is its diffusion coefficient in bulk hydrocarbon. The partition coefficients are by far the major determinants of the relative magnitudes of the permeability coefficients; the diffusion coefficients make only a minor contribution. We note that the recent emphasis on theoretically calculated intramembranous diffusion coefficients (Dm'S) has diverted attention from the experimentally measurable and physiologically relevant permeability coefficients (Pd'S) and has obscured the simplicity and usefulness of Overton's rule.

Experimental evidence that mutual and tracer diffusion coefficients for hemoglobin are not equal

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)

Diffusion in protein solutions at high concentrations: A study by quasielastic light scattering spectroscopy

Quasielastic light scattering spectroscopy was used to study the mutual diffusion coefficient Dm of bovine serum albumin over the pH range 4.3–7.6 for concentrations ranging as high as 334 g/l. Using literature measurements of the tracer diffusion coefficient DT and the osmotic compressibility (∂π/∂c)P,T, we find that Dm depends on concentration and pH as predicted by the generalized Stokes–Einstein relation Dm=DT(∂π/∂c)P,T (1−φ)/KBT, φ being the volume fraction of solute and KB being Boltzmann’s constant. Our data show that Dm and DT depend quite differently on solute concentration; DT can be a factor of 3 smaller than Dm at protein concentrations exceeding 200 g/l.

Kinetics of surface smoothing in uranium monocarbide single crystals

The relaxation of sinusoidal profiles to flatness on the (110) surfaces of nearly stoichiometric uranium monocarbide single crystals has been determined between 1800 and 2160° C in a helium atmosphere. From the wavelength dependence of the relaxation constants, it was established that the mass-transfer rate due to capillary forces is primarily controlled by volume diffusion in the lattice. The diffusion coefficient Dm associated with the relaxation process is given by the Arrhenius relation Dm = Do exp (−Q/RT), with Do=(3.6±2.0)×10−3 cm2/sec and the activation energy Q=72.2 ±2.9 kcal/mole. These values are compared with the published tracer and mass-transfer diffusion data on uranium monocarbide. Faceting of profiles occurred after annealing in helium on the (100) and (111) surfaces indicating the presence of cusps in the surface-energy plot at these orientations.