Apparent self-diffusion coefficient

Figure 5.3 depicts the Arrhenius plots of the apparent self-diffusion coefficient of the cation (Dcation) and anion (Oanion) for EMIBF4 and EMITFSI (Figure 5.3a) and for BPBF4 and BPTFSI (Figure 5.3b). The Arrhenius plots of the summation (Dcation + f anion) of the cationic and anionic diffusion coefficients are also shown in Figure 5.4. The fact that the temperature dependency of each set of the self-diffusion coefficients shows convex curved profiles implies that the ionic liquids of interest to us deviate from ideal Arrhenius behavior. Each result of the self-diffusion coefficient has therefore been fitted with VFT equation [6].

TABLE 5.3 VFT Equation Parameters for Apparent Self-Diffusion Coefficient Data, D = Doexp[-S/(T - To)]... 

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. 

Fig. 21.4. QNS spectra of a 3.2 M H2SO4 solution at 263 K taken at various scattering angles with a resolution of 19 peV (INS instrument of the Laue-Langevin Institute, Grenoble) . The momentum transfer value at fico = 0 is indicated for each spectrum. The experimental points are compared with a theoretical S(Q, co) dashed curve corresponding to the convolution of the resolution function by a single translational lorentzian characterizing the mean water self-diffusion D, = 0.532 x 10 cm s" and with a convolution of the latter by a fast translational motion involving 12% of the protons (solid line). The fast motion is characterized by an apparent self-diffusion coefficient D = 2.2 x 10" cm s at 263 K.

Here, the apparent self-diffusion coefficient D pp of the alcohol in the ternary system can be measured by the NMR spin-echo technique [6]. is the selfdiffusion coefficient of the alcohol within or associated with the micelles and the corresponding value in the aqueous pseudophase it is approximated by measuring the self-diffusion coefficient in the binary D20-pentanol system. As is much smaller than the partition coefficient p can be approximated by... 

Fig. 3. Apparent self-diffusion coefficient of cyclohexane Cg Hi 2 adsorbed on silica, 90 A, 10p(gs) as a function of coverage.

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... 

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

Self-diffusivity, cooperatively with ionic conductivity, provides a coherent account of ionicity of ionic liquids. The PGSE-NMR method has been found to be a convenient means to independently measure the self-diffusion coefficients of the anions and the cations in the ionic liquids. Temperature dependencies of the self-diffusion coefficient, viscosity and ionic conductivity for the ionic liquids, cannot be explained simply by Arrhenius equation rather, they follow the VFT equation. There is a simple correlation of the summation of the cationic and the anionic diffusion coefficients for each ionic liquid with the inverse of the viscosity. The apparent cationic transference number in ionic liquids has also been found to have dependence on the... 

Zelsmann and co-workers [88] have reported tracer diffusion coefficients for water in Nafion membranes exposed to water vapor of controlled activity. These were determined by various techniques, including isotopic exchange across the membrane. They reported apparent self-diffiision coefficients of water much lower than those determined by Zawodzinski et al. [64], with a weaker dependence on water content, varying from 0.5 x 10 cm to 3 x 10 cm /s as the relative humidity is varied from 20 to 100%. It is likely that a different measurement method generates these large differences. In the experiments of Zelsmaim et al., water must permeate into and through the membrane from vapor phase on one side to vapor phase on the other. Since the membrane surface in contact with water vapor is extremely hydrophobic (see Table 7), there is apparently a surface barrier to water uptake from the vapor which dominates the overall rate of water transport in this type of experiment. 

Fig. 21 Steady state incoherent intermediate scattering functions d> (r) as functions of accumulated strain yt for various shear rates y the data were obtained in a col loidal hard sphere dispersion at packing fraction

Fig. 19. Apparent self-diffusion constants Oapp of the triglyceride oil component in a nanocapsule dispersion derived from the plots in Fig. 18. For short diffusion times A, the values for Dapp come close to the self-diffusion coefficient of the hulk oil D = 2.3X10 m /s, top line). For long...

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, Dmic, was approximated by the measured self-diffusion 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... 

Incoherent flow is often referred to as pseudo-diffusion. An apparent diffusion coefficient which can be significantly bigger than the self-diffusion coefficient is then defined. Pulse sequences to measure coherent flow (figure B 1.14.9) can also be used for (spatially) incoherent motion although the theory has to be reconsidered at this point [M, M and M] ... 

To make the significance of the NMR technique as an experimental tool in surfactant science more apparent, it is important to compare the strengths and the weaknesses of the NMR relaxation technique in relation to other experimental techniques. In comparison with other experimental techniques to study, for example, microemulsion droplet size, the NMR relaxation technique has two major advantages, both of which are associated with the fact that it is reorientational motions that are measured. One is that the relaxation rate, i.e., R2, is sensitive to small variations in micellar size. For example, in the case of a sphere, the rotational correlation time is proportional to the cube of the radius. This can be compared with the translational self-diffusion coefficient, which varies linearly with the radius. The second, and perhaps the most important, advantage is the fact that the rotational diffusion of particles in solution is essentially independent of interparticle interactions (electrostatic and hydrodynamic). This is in contrast to most other techniques available to study surfactant systems or colloidal systems in general, such as viscosity, collective and self-diffusion, and scattered light intensity. A weakness of the NMR relaxation approach to aggregate size determinations, compared with form factor determinations, would be the difficulties in absolute calibration, since the transformation from information on dynamics to information on structure must be performed by means of a motional model. 

Table I shows self-diffusion coefficients (T = 300 K) for the three interlayer cations in low-order hydrates of montmorillonite, as calculated conventionally from the slopes of graphs of the (three-dimensional) mean-square cation displacement versus time (8, 16-18). Experimental values of the cation self-diffusion coefficients in aqueous solution also are listed (32). It is apparent that monovalent cation mobility in the one-layer hydrate is at best a few percent of that in bulk aqueous solution, and that the mobility increases significantly with increasing water content, to approach about 25% of the bulk-solution value in the three-layer hydrate. The constrained geometry and the charge sites on the clay mineral surface thus act to retard significantly the diffusive motions of interlayer cations through adsorbed water.

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