Diffusion coefficients, values

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. 

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... 

Self-difFusion coefficients were measured with the NMR spin-echo method and mutual diffusion coefficients by digital image holography. As can be seen from Figure 4.4-3, the diffusion coefficients show the whole bandwidth of diffusion coefficient values, from 10 m s on the methanol-rich side, down to 10 on the [BMIM][PFg]-rich side. The concentration dependence of the diffusion coefficients on the methanol-rich side is extreme, and shows that special care and attention should be paid in the dimensioning of chemical processes with ionic Hquids. 

Diffusion coefficient values for HN03 ranging from 0.12 to 0.15 cm2/s have been reported. Trapping media for HN03 include MgO (38), Na2C03 (42), Na2C03-glycerol (43), NaCl (44, 39), NaF (45), and anodized aluminum (46). 

MacFarlane et al. [129] and Watanabe et al. [24a, 114] discussed the difference in diffusivity of component ions. Reported diffusion coefficients of ILs are shown in Table 3.19 together with viscosity and ionic conductivity. From that table, it is easy to see that lower viscosity ILs show larger diffusion coefficients and higher ionic conductivity. Cations generally have larger diffusion coefficient values than do anions in ILs. This means that the cation diffuses more easily than the anion. However, the transference numbers of onium cation (t+) in ILs calculated from the results of PFG-NMR is in the range 0.5 to 0.6 and their contribution to the ionic conductivity is mostly the same, irrespective of the ion species. In the case of [bpy][BF4], the BF4- shows a larger diffusion coefficient than that of bpy+, and therefore t+ is below 0.5 [24a], Thus, as well as thermal and electrochemical properties, the diffusion behavior of component ions is dependent on their structure. 

Correcting for the 50% degree of crystallinity using Eq. (9-21 b) leads to the final estimated diffusion coefficient values ... 

Table 9-6 gives the permeability coefficients for a series of organic compounds in LDPE at various temperatures (Salame, 1961). A collection of diffusion coefficient values for organic substances in polyolefins are given in Appendix I. 

Reference lists are added at the end of each chapter reflecting the nature of the chapter being mainly a review or of a descriptive character. A comprehensive list of citations follows the large collection of diffusion coefficient values in Appendix I. In the first introductory chapter a list of useful secondary literature is given which contains many additional papers. Nevertheless, the authors are aware that many valuable references were not cited in this work. 

An attempt was made by Doblhofer et al. [210] to separate surface from bulk charging processes for thermally prepared Ru02 using the potential step technique. These authors [210] concluded that some bulk diffusion was involved, presumably involving protons, and estimated a diffusion coefficient of 10 19 cm2 s1. Weston and Steele [213] deduced a diffusion coefficient value for protons in porous powder electrodes of Ru02 which is approximately similar to the value of Doblhofer et al. [210]. Iwakura and co-workers [214], on the other hand, employed cyclic voltammetry in deduc-... 

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 ... 

Experimental results from our previous studies [26] demonstrated that the diffusional resistance in the liquid phase is negligible under representative experimental conditions and intramembrane transport is the rate-limiting step for the alum recovery process. The following provides a stepwise protocol for the determination of self-diffusion coefficient values and the alum recovery rate for the DMP. 

Step 4 Determination of membrane phase self-diffusion coefficient values Equation 34.20c can be arranged as follows ... 

Further to this, another experiment was carried out (Run 2). In this experiment, the feed volume was changed to 3 L (from 6 F in Run 1), sweep volume to 1 L (from 1.5 L), and the membrane area to 370 cm (from 415 cm ). It was observed that the sweep side concentration profile for these self-diffusion coefficient values matched reasonably well with the experimental findings [51]. The results are shown in Figure 34.22c. The self-diffusion coefficient of H" " ions has been investigated earlier... 

Nafion 117 were compared with the values in the aqueous phase at infinite dilution [53], the ratio of />Nafion ii7/f inflnite ditmion was found to be 1/41 and 1 /93 for and Al ions, respectively. Miyoshi [32] had earlier found in their work with Na, K, Ca, Cu, and ions during DMP that the drop in self-diffusion coefficient value in the membrane phase was higher for the bivalent ions than for the monovalent ions. This point can be understood from the fact that in their movement across the membrane, trivalent ions have to link themselves with three negative sites, to maintain electroneutrality, while monovalent ions need to link with only one negative site. Therefore, the efficiency with which a multivalent ion hops within an exchange membrane is significantly reduced in comparison with monovalent ions. 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

Diffusion Coefficient Value Comparison in Nafion 117 and lonac MC 3470... 

Two experiments were carried out. Run 1 is the standard run and is the basis for generation of Figure 34.24a. In Run 2, a 2 L sweep solution was used instead of 1 L to verify the findings from Run 1. The findings from the model are presented in Figure 34.24b. The self-diffusion coefficient values were determined to be... 

Even for lonac MC 3470, it was the H" " ion that was the trace species. A comparison of the diffusion coefficient values for the two membranes is presented in Table 34.3. From this table, it can be observed that the self-diffusion coefficient values for aluminum and hydrogen ions are similarly lowered as the experimental interdiffusion coefficient value. This lowering is about one order for both the cases. Explanation for low Dai,h values in the heterogeneous membrane is desired, as it explains the slow transport kinetics in heterogeneous membrane. 

However, Nafion-modified electrodes also exhibited several disadvantages. For example, the response time of the Nafion-coated sensors increases due to a reduced diffusion coefficient value in the film [7], This can pose a serious disadvantage for in vivo work where dopamine and other neurotransmitter releases often occur on a sub-second time scale. In addition, Nafion coatings perform well for applications such as stripping analysis, but their use for direct voltammetric analysis is complicated by slow equilibration of the film with solution species [5 7], Therefore, there is a need for a modification system that can allow for rapid and selective permeation of the ions of interest. 

Geus et al. [75] reports diffusion data at 21 and 145°C for Hj, N2, CH4, CO2 and CF2CI2 in silicalite membranes on a clay support which are obtained with the similar transient permeation technique as used above by Vroon. The diffusion coefficients for methane are about two orders of magnitude smaller than those obtained by PF-NMR methods. Usually this last technique gives relatively large diffusion coefficient values, which in the case of n-butane are of the same order of magnitude as reported for FR techniques and membrane techniques as reported by Kapteyn. 

Fig. 15 Normalized diffusion coefficients D(q 0)/Do as functions of the volume fraction for PMMA-grafted silica particles DP 150 open square) and DP 760 (open circle) in CCL4 (good solvent for PMMA) at 2(FC [208]. The different crossover concentrations in the dynamics are indicated by solid and vertical arrows. The inset shows in magnification the area bounded by the rectangle around a normalized diffusion coefficient value of 1 in the main plot, using the same colors and symbols (solid ) for the two systems. Lines are drawn to guide the eye...

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