Diffusivity data

It appears that a loose interpretation of this type may be the origin of a discrenancy found by Otanl and Smith [59] in attempting to apply effective diffusivities from Wakao and Smith s [32] isobaric diffusion data to measurements on a chemically reacting system. This was pointed out by Steisel and Butt [60], and further pursued to the point of detailed computer modeling of a particular pore network by Wakao and Nardse [61]. 

We shall see in Sec. 9.10 that sedimentation and diffusion data yield experimental friction factors which may also be described-by the ratio of the experimental f to fQ, the friction factor of a sphere of the same mass-as contours in solvation-ellipticity plots. The two different kinds of contours differ in detailed shape, as illustrated in Fig. 9.4b, so the location at which they cross provides the desired characterization. For the hypothetical system shown in Fig. 9.4b, the axial ratio is about 2.5 and the protein is hydrated to the extent of about 1.0 g water (g polymer)". ... 

As a result of these difficulties the reported diffusivity data show many apparent anomaUes and inconsistencies, particularly for 2eohtes and other microporous adsorbents. Discrepancies of several orders of magnitude in the diffusivity values reported for a given system under apparendy similar conditions are not uncommon (18). Since most of the intmsive effects lead to erroneously low values, the higher values are probably the more rehable. 

Gaseous diffusion and thermal diffusion data may be found in References 8 and 9. 

Sun-Chen examined tracer diffusion data of aromatic solutes in alcohols up to the supercritical range and found their data correlated with average deviations of 5 percent and a maximum deviation of 17 percent for their rather hmited set of data. 

Catchpole-Kinp examined binaiy diffusion data of near-critical fluids in the reduced density range of 1 to 2.5 and found that their data correlated with average deviations of 10 percent and a maximum deviation of 60 percent. They observed two classes of behavior. For the first, no correction fac tor was required R = 1). That class was comprised of alcohols as solvents with aromatic or ahphatic solutes, or carbon dioxide as a solvent with ahphatics except ketones as solutes, or... 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

Vigne.s empirically correlated mixture diffusivity data for 12 binary mixtures. Later Ertl et al. evaluated 122 binary systems, which showed an average absolute deviation of only 7 percent. None of the latter systems, however, was veiy nonideal. 

Of the parameters making up the Hatta number, hquid diffusivity data and measurement methods are weh reviewed in the hterature. 

Smithells Metals Reference Book, 7th edition, Butterworth-Heinemann, 1992 (for diffusion data). 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

The chromatography literature contains a vast amount of dispersion data for all types of chromatography and, in particular, much of the data pertains directly to GC and LC. Unfortunately, almost all the data is unsuitable for validating one particular dispersion equation as opposed to another. There are a number of reasons for this firstly, the necessary supporting data (e.g., diffusivity data for the solutes in the solvents employed as the mobile phase, accurate distribution and/or capacity factor constants (k")) are not available secondly, the accuracy and precision of much of the data are inadequate, largely due to the use of inappropriate apparatus with high extracolumn dispersion. 

Katz and Scott used equation (7) to calculate diffusivity data from measurements made on a specially arranged open tube. The equation that explicitly relates dispersion in an open tube to diffusivity (the Golay function) is only valid under condition of perfect Newtonian flow. That is, there must be no radial flow induced in the tube to enhance diffusion and, thus, the tube must be perfectly straight. This necessity, from a practical point of view, limits the length of tube that can be employed. 

W. Brown, R. Johnsen, P. Stilbs, B. Lindman. Size and shape of nonionic amphiphile (Ci2Eg) micelles in dilute aqueous solutions as derived from quasielastic and intensity of light scattering, sedimentation and pulsed-field-gradient nuclear magnetic resonance self-diffusion data. J Phys Chem 87 4548-4553, 1983. 

The need to predict mutual diffusion coefficients from self-diffusion coefficients often arises, and many efforts have been made to understand and predict mutual diffusion data, through approaches such as, for example, the following extension of the Darken equation [5j ... 

Good reliable diffusion data is difficult to obtain, particularly over a wide range of temperature. The Gilliland relation is [63] ... 

Table 5. Chemical diffusion data for lithium-tin phases at 25 °C.

The kinetics of ion backspillover on the other hand will depend on two factors On the rate, I/nF, of their formation at the tpb and on their surface diffusivity, Ds, on the metal surface. As will be shown in Chapters 4 and 5 the rate of electrochemically controlled ion backspillover is normally limited by I/nF, i.e. the slow step is their transfer at the tpb. Surface diffusion is usually fast. Thus, as shown in Chapter 5, for the case of Pt electrodes where reliable surface O diffusivity data exist, obtained by Gomer and Lewis several years ago,76 Ds is at least 4.-10 11 cm2/s at 400°C and thus an O2 ion can move at least 1 pm per s on a Pt(lll) or Pt(110) surface. Therefore ion backspillover from solid electrolytes onto electrode surface is not only thermodynamically feasible, but can also be quite fast on the electrode surface. But does it really take place This we will see in the next Chapter. 

For gases, both permeation and diffusion data are best measured by permeation tests, many different types been described elsewhere. The same sheet membrane permeation test can quantify permeation coefficient Q, diffusion coefficient D, solubility coefficient s, and concentration c. The membrane, of known area and thickness, must be completely sealed to separate the high-pressure (initial) region from that containing the permeated gas it may need an open-grid support to withstand the pressure. The permeant must be suitably detected and quantified (e.g., by pressure or volume buildup, infrared (IR) spectroscopy, ultraviolet (UV), gas chromatography, etc.). 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Shen Q, Ren H, Fisher M, Bouley J, Duong TQ. Dynamic tracking of acute ischemic tissue fates using improved unsupervised isodata analysis of high-resolution quantitative perfusion and diffusion data. J Cereb Blood Flow Metab. 2004 24 887-897. 

Self-diffusion data [37] derived from NMR PGSE measurements for decane, water, and AOT are illustrated in Fig. 3. The self-diffusion of decane decreases gradually as a decreases from 1.0 to 0.3. The magnitude of decane self-diffusion suggests that the microstructure remains substantially continuous in decane over this composition range. Both water and AOT diffusion initially decrease as a decreases. One can readily see that in this... 

FIG. 3 Self-diffusion coefficients of decane (A), water (B), and AOT ( ) in brine, decane, and AOT microemulsions at 45°C as a function of decane weight fraction, a (relative to decane and brine). Breakpoints in the self-diffusion data for both water and AOT are observed at a = 0.85 and at 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)... 

FIG. 4 Apparent mole fraction (x) water in continuous phase of brine, decane, and AOT microemulsion system derived from the water self-diffusion data of Fig. 3 using the two-state model of Eq. (1). 

FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase. 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. was found to be... 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

The side-by-side diffusion cell has also been calibrated for drug delivery mass transport studies using polymeric membranes [12], The mass transport coefficient, D/h, was evaluated with diffusion data for benzoic acid in aqueous solutions of polyethylene glycol 400 at 37°C. By varying the polyethylene glycol 400 content incrementally from 0 to 40%, the kinematic viscosity of the diffusion medium, saturation solubility for benzoic acid, and diffusivity of benzoic acid could be varied. The resulting mass transport coefficients, D/h, were correlated with the Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc) according to the relationships... 

---