Diffusivity experimental values

Diffusivity correfations for gases are outhned in Table 5-14. Specific parameters for individual eqiiations are defined in the specific text regarding each equation. References are given after Table 5-19. The errors reported for Eq. (5-194) through (5-197) were compiled by Reid et al., who compared the predictions with 68 experimental values of D g. Errors cited for Eqs. (5-198) to (5-202) were reported by the authors. 

Fuller-Schettler-Giddings The parameters and constants for this correlation were determined by regression analysis of 340 experimental diffusion coefficient values of 153 binary systems. Values of X Vj used in this equation are in Table 5-16. 

If a straight line such as curve B of Fig. 12-43 represents the experimental data and if it has been established that the drying time varies inversely as the square of the thickness, the average hquid diffusivity can be obtained as follows. At a given value of (W — W )/ W — W ), read the corresponding value of DS/d from cui ve A, Eq. (12-32), Fig. 12-43. At the same value of (W - WJ/(W - WJ, read the corresponding experimental value of 0 from cui ve B (upper scale). Then... 

Q/d-) experimental where = average experimental value of liquid diffusivity, mVh. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

After scaling, the predicted frequencies are generally within the expected range for carbonyl stretch (-1750 cm ). The table below reproduces our values, published theoretical values using the 6-31+G(d) basis set (this basis set includes diffuse functions), and the experimental values, arranged in order of ascending experimental frequency ... 

The values in red are within O.OlA of the experimental value. Using the 6-31G basis set, including diffuse functions on the hydrogen atom, improves the result over that obtained with diffuse functions only on the fluorine atom, although the best result with this basis set is obtained with no diffuse functions at all. 

The experimental value for Agl is 1.97 FT cirT1 [16, 3], which indicates that the silver ions in Agl are mobile with nearly a thermal velocity. Considerably higher ionic transport rates are even possible in electrodes, by chemical diffusion under the influence of internal electric fields. For Ag2S at 200 °C, a chemical diffusion coefficient of 0.4cm2s, which is as high as in gases, has been measured... 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

Experimental values of diffusivities are given in Table 10.2 for a number of gases and vapours in air at 298K and atmospheric pressure. The table also includes values of the Schmidt number Sc, the ratio of the kinematic viscosity (fx/p) to the diffusivity (D) for very low concentrations of the diffusing gas or vapour. The importance of the Schmidt number in problems involving mass transfer is discussed in Chapter 12. 

A method, proposed more recently by FULLER, SCHETTLER and GlDDlNGSf8 . is claimed to give an improved correlation. In this approach the values of the diffusion volume have been modified to give a better correspondence with experimental values, and have then been adjusted arbitrarily to make the coefficient in the equation equal to unity. The method does contain some anomalies, however, particularly in relation to the values of V for nitrogen, oxygen and air. Details of this method are given in Volume 6. 

Values of the diffusivities of various materials in water are given in Table 10.7. Where experimental values are not available, it is necessary to use one of the predictive methods which are available. 

Mathai and Singh have estimated the permeability coefficient P, using the formula P = kD where k is the partition coefficient and D is the diffusivity. They have used both parallel and series models to calculate P. The experimental values are always greater than measured values. The poor agreement between the experimental and calculated values is attributed to the polar-polar interaction between the epoxy group and nitrile group. 

The values for the lipid molecules compare well (althoughJgiey are still somewhat larger) with the experimental value of 1.5x10 cm /s as measured with the use of a nitroxide spin label. We note that the discrepancy of one order of magnitude, as found in the previous simulation with simplified head groups, is no longer observed. Hence we may safely conclude that the diffusion coefficient of the lipid molecules is determined by hydrodynamic interactions of the head groups with the aqueous layer rather than by the interactions within the lipid layer. The diffusion coefficient of water is about three times smaller than the value of the pure model water thus the water in the bilayer diffuses about three times slower than in the bulk. 

The self-diffusion coefficient calculated for the three body potential is Z) = 1.3 X lO cm /sec. This is to be compared with the experimental value of 2.3 x 10" cmVsec and to the value of 2.25 x 10 cm /sec for the two-body liquid. It could be said that the three-body liquid shows more rigidity in some sense than the two-body liquid. 

The accuracy of constant k has been evaluated by comparing the experimental values of 0(t) with the values deduced from Eq. (28) for contact times greater than 30 minutes shown in Table 1. Good agreement between both series of values justifies the simple model of diffusion of TCP in silicone rubber. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

Experimental values for the more common systems can be often found in the literature, but for most design work the values will have to be estimated. Methods for the prediction of gas and liquid diffusivities are given in Volume 1, Chapter 10 some experimental values are also given. 

The values derived in this way for the diffusion coefficients exhibit surprising agreement with the experimental values, even for small ions, better than a coincidence in the order of magnitude. More detailed theoretical analysis indicates that the formation of holes required for particle jump is analogous to the formation of holes necessary for viscous flow of a liquid. Consequently, the activation energy for diffusion is similar to that for viscous flow. 

Diffusion in a sphere may be more common than that in a cylinder in the pharmaceutical sciences. The example we may think of is the dissolution of a spherical particle. Since convection is normally involved in solute particle dissolution in reality, the dissolution rate estimated by considering only diffusion often underestimates experimental values. Nevertheless, we use it as an example to illustrate the solution of the differential equations describing diffusion in the spherical coordinate system [1],... 

The measured value of k Sg is 0.716 cm3/(sec-g catalyst) and the ratio of this value to k ltTueSg should be equal to our assumed value for the effectiveness factor, if our assumption was correct. The actual ratio is 0.175, which is at variance with the assumed value. Hence we pick a new value of rj and repeat the procedure until agreement is obtained. This iterative approach produces an effectiveness factor of 0.238, which corresponds to a differs from the experimental value (0.17) and that calculated by the cylindrical pore model (0.61). In the above calculations, an experimental value of eff was not available and this circumstance is largely responsible for the discrepancy. If the combined diffusivity determined in Illustration 12.1 is converted to an effective diffusivity using equation 12.2.9, the value used above corresponds to a tortuosity factor of 2.6. If we had employed Q)c from Illustration 12.1 and a tortuosity factor of unity to calculate eff, we would have determined that rj = 0.65, which is consistent with the value obtained from the straight cylindrical pore model in Illustration 12.2. 

---