Temperature apparent diffusion coefficients

The above data relate to very pure iron samples with low dislocation densities. In real steels the trapping effects result in much lower apparent diffusivities, which are dependent on the metallurgical state of the steel, as well as its chemical composition. Typical values for the apparent diffusion coefficient of hydrogen in high-strength alloy steel at room temperature are in the region of 10" mVs. 

More than one point defect species may be present in a crystal at any temperature, and the amount of matter transported by diffusion will depend upon the number of each defect type present. In general, therefore, the overall apparent diffusion coefficient, D, will be the sum of the individual contributions, for example ... 

Fig. 20. Temperature dependence of the apparent diffusion coefficient of NIPA gel...

This shows that the mean of the temperature wave moves with the kinematic wave velocity and that an apparent diffusion coefficient may be defined to describe the dispersion. This coefficient is the sum of the diffusion coefficients which would be obtained if each effect were considered independently. Such an additivity has been demonstrated by the author for the molecular and Taylor diffusion coefficients elsewhere (Aris 1956) and is assumed in a paper by Klinkenberg and others (van Deemter, Zuiderweg Klinkenberg 1956) in their analysis of the dispersion of a chromatogram. 

Figures 14-1 and 14-2 show estimations of shelf life in a 7.5 g PS containing portion pack before two different taste threshold concentrations (2 and 0.1 mg/kg) of styrene are exceeded in the product. In each graph the diffusion coefficients from Linssen et al. (1992) for a 1 1 PS HIPS polymer blend at room temperature (23 °C) and refrigeration temperature (4 °C) are used. The estimation using Eq. (14-5) at 23 °C and 4 °C and an calculated apparent diffusion coefficient for PS/PE and PS/EVOH/PE structures (see Table 14-3) are used in Eq. (14-4) (see example 14-5) to calculate the days before a styrene taint is detected in the product. The shelf life is decreased by a factor of the square of the increase in the material s residual styrene content. As seen in Figures 14-1 and 14-2 a reduction in the taste threshold by a factor of ten means almost a 100 times decrease in the shelf life.

Results are shown in Figs. 12 and 13. All blend specimens were set iso-thermally above LCST and kept there for a maximum of 5 min. As will be seen, this corresponds only in some cases to an early stage of spinodal decomposition depending on temperature. The diffusion coefficients governing the dynamics of phase dissolution below LCST are in the order of 10"14 cm2 s"1. Figure 12 reflects the influence of the mobility coefficient on the phase dissolution. As can be seen, the apparent diffusion coefficient increases with increasing temperature of phase dissolution which expresses primarily the temperature dependence of the mobility coefficient. Furthermore, it becomes evident that the mobility obeys an Arrhenius-type equation. Similar results have been reported for phase dis-... 

Fig. 12. Arrhenius plot of the apparent diffusion coefficient for PMMA/SAN-31.5(50/50)(31.5 wt% AN in SAN). The apparent diffusion coefficients results after temperature jumps from 210°C to different annealing temperatures below the LOST (cf. Fig. 1 la). Phase separation of the blend starts at 200 JC...

It is difficult to make an exhaustive list of the applications of quantitative imaging, because a large number of parameters are quantifiable proton density, relaxation time T, T2, T2 or T 2, T p), data qualifying interaction of pools by magnetization transfer, apparent diffusion coefficients, indices characterizing diffusion phenomena from tensor estimation or a (/-space approach, temperature difference, static magnetic field, B1 field amplitude, current density or values related to dynamic MRI contrast agent uptake. 

Figure 13. Temperature dependence of apparent diffusion coefficient of water vapor in newborn rat stratum corneum, 0 to 75% RH vapor gradient. Open circles, supported membrane closed circles, unsupported membrane. Thickness assumed constant for the purposes of calculation.

An extended analysis of data using the time-derivative method provides for simultaneous determination of apparent sedimentation, and apparent diffusion coefficient, values at a particular concentration and temperature [9]. The apparent diffusion coefficient was calculated from the apparent sedimentation coefficient distribution by the following relationship ... 

Fig. 23 Temperature dependence of the (apparent) diffusion coefficients measured with PFG-NMR obtained by fitting the integrals of the most shielded methyl signal for the cooling and the heating regime. The error bars correspond to the statistical error of D obtained during the fitting procedure. For the other spectral regions (amide and aliphatic region) similar behaviour was observed. Reproduced from Brand et al. (2006) with kind permission from American Chemical Society.

Figure 3. The ratio jx/Mo can be obtained from the ratio of the apparent diffusion coefficients measured on cylindrical and spherical gels. The theoretical curve is obtained from equation 12. The two experimental points correspond to a polyacrylamide gel in water (circle) and a polydimethylsiloxane gel in toluene (box). The temperature was 22 °C.

The self-diffusion coefficients reflect the molecular mobility in solution and are sensitive to temperature, solvent viscosity, and molecular mass. Similarly to other spectral parameters, the apparent self-diffusion coefficient is the weighted average for all species remaining in the equilibrium. Thus, when a small guest molecule interacts with a bigger host molecule its apparent diffusion coefficient decreases, allowing us to detect the formation of an inclusion complex. Moreover, the dependence of the self-diffusion coefficient of guest on the host molar fraction allows us to determine the association constant similarly to the chemical shift titration. 

A more sensitive and reliable test for the presence of convection is to record two or more diffusion experiments with differing values of the diffiision period A under otherwise identical conditions. In the absence of convection (or where its influence has been suppressed), the value of D obtained should not differ between data sets. In contrast, the apparent diffusion coefficients measured in the presence of convection will vary with A, as indicated by Eq. (9.11), and produce progressively larger values of />app with longer diffusion periods. This influence is readily apparent for quinine 9.1 in CDCI3 recorded at the slightly elevated temperature of 313 K but may also be observed at a much reduced level at 298 K where probe temperature regulation is employed (Fig. 9.12). 

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