Self compared with transport diffusivity

Despite extensive work in the last decade, large discrepancies still persist between the various experimental techniques which measure diffusion in zeohtes. One of the difficulties is that one has to compare self-diffusivities, obtained by PFG NMR or QENS methods, with transport diffusivities derived from macroscopic experiments. The transport diffusivity is defined as the proportionahty factor between the flux and a concentration gradient (Fick s first law)... 

The methods described so far for studying self-diffusion are essentially based on an observation of the diffusion paths, i.e. on the application of Einstein s relation (eq 3). Alternatively, molecular self-diffusion may also be studied on the basis of the Fick s laws by using iso-topically labeled molecules. As in the case of transport diffusion, the diffusivities are determined by comparing the measured curves of tracer exchange between the porous medium and the surroundings with the corresponding theoretical expressions. As a basic assumption of the isotopic tracer technique for studying self-diffusion, the isotopic forms are expected to have... 

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. 

The results described in this report compare well with data of Van-Den-Begin et al. [15] obtained on silicalite samples with an equivalent radius of 31pm by means of Single-Step Frequency-Response. The authors report a self diffusion coefficient for n-hexane of about 2 10 cmVs at a temperature of444 K. However, it has to be considered that, due to the shape of the sorption isotherm, the self-diffusion coefficient will be somewhat smaller than the transport diffusion coefficient. Caro et al [16] report a transport diffusion coefficient of 1.8 10 cmVs for the system n-hexane/HZSM-5 at 298 K, determined gravimetrically. The crystals used in that study were of prismatic shape, the dimensions being 330 pm (z-axis), 110 pm... 

NMR PFG measurements determine the tracer or self-diffusivity (D ) under equilibrium conditions with no concentration gradient. n any sorption rate measurement it is the transport diffusivity under the influence of a concentration gradient which is measured. In general these two quantities are not the same but the relationship between them can be established from irreversible thermodynamics. (17,18) In the low concentration limit the thermodynamic correction factor vanishes and the transport and self diffusivities should approach the same limit. Since ZLC measurements are made at low concentrations within the Henry s Law region the diffusivity values should be directly comparable with the NMR self-dif fusivities. ... 

As an example, see Skoulidas et al. [2]. They reported atomistic simulations for both self- and transport diffusivities of light gases in carbon nanotubes and compared them with transport rates in zeolites with comparable pore sizes. 

Semiconductor compounds Me gX (where Me = Cu, Ag and X = S, Se, Te) display a wide variety of physical and physical and chemical properties, that makes them promising for electronic equipment [1, 2]. A wide range of electrical and thermal properties, the ability to control these properties via controlled deviation fi om stoichiometry and high parameters of ion transport facilities make them convenient for the study of transport phenomena in mixed ionic and electronic conductors [3-5]. It should be noted that high cation conductivity and high value of self-difiusion coefficients are comparable with the conductivity and diffusion in liquid electrolytes and appear against the predominant electronic conductivity [6-8]. 

Equilibrium MD simulations of self-diffusion coefficients, shear viscosity, and electrical conductivity for C mim][Cl] at different temperatures were carried out [82] The Green-Kubo relations were employed to evaluate the transport coefficients. Compared to experiment, the model underestimated the conductivity and self-diffusion, whereas the viscosity was over-predicted. These discrepancies were explained on the basis of the rigidity and lack of polarizability of the model [82], Despite this, the experimental trends with temperature were remarkably well reproduced. The simulations reproduced remarkably well the slope of the Walden plots obtained from experimental data and confirmed that temperature does not alter appreciably the extent of ion pairing [82],... 

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