Diffusion coefficient evaluation

Thus, in spite of a satisfactory agreement of Equation 17 with experimental data for systems with weakly convex adsorption isotherms, the internal diffusion coefficients, evaluated for these cases according to Equation 17, are in fact below their actual value. 

Fig. 37 The dependence of diffusion coefficient evaluated for O2 in irradiated PP films. The data were taken from [95E1]. Absorbed 7 ( °Co)-dose 25 kGy dose rate 0.6 kGy.h . ...

Table 8.6 Effective diffusion coefficients evaluated by different methods.

Fig. 79. Arrhenius plot of the diffusion coefficients evaluated from the description of the kinetics of solid-state ion exchange in the systems CuCl/Na-Y and CuCl/Na-M through a diffusion model (for details, see text after [289], with permission)...

If very broad, the molecular weight distribution may influence the (average) center-of-mass diffusion coefficient evaluated from echo attenuation curves [169, 175]. 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

Assuming that Eq. (2.67) applies to small molecules in the limit as n 1, calculate To, using D = 3 X 10" m sec" for a typical low molecular weight molecule. Use this value of Tq to estimate t for a polymer with n = 10. Based on Eq. (2.63), evaluate diffusion coefficient for bulk... 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

In a binary gas mixture, the diffusion coefficient of the species i at a mole fraction jc, widr respect to tlrat of the species j is given after evaluating the constants by tire equation... 

The behavior of ionic liquids as electrolytes is strongly influenced by the transport properties of their ionic constituents. These transport properties relate to the rate of ion movement and to the manner in which the ions move (as individual ions, ion-pairs, or ion aggregates). Conductivity, for example, depends on the number and mobility of charge carriers. If an ionic liquid is dominated by highly mobile but neutral ion-pairs it will have a small number of available charge carriers and thus a low conductivity. The two quantities often used to evaluate the transport properties of electrolytes are the ion-diffusion coefficients and the ion-transport numbers. The diffusion coefficient is a measure of the rate of movement of an ion in a solution, and the transport number is a measure of the fraction of charge carried by that ion in the presence of an electric field. 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

Fig. 20.21 J-l transients for the permeation of hydrogen through ferrous alloys. The normal transient enables the diffusion coefficient ) to be evaluated from the relationship /, = L /6D, where /, is the time at which J attains a value of 0-63 of the steady-state permeation J...

The chemical diffusion coefficient in that phase was also evaluated and found to... 

The task of the problem-independent chemistry software is to make evaluating the terms in Equations (6-10) as straightforward as possible. In this case subroutine calls to the Chemkin software are made to return values of p, Cp, and the and hk vectors. Also, subroutine calls are made to a Transport package to return the ordinary multicomponent diffusion matrices Dkj, the mixture viscosities p, the thermal conductivities A, and the thermal diffusion coefficients D. Once this is done, finite difference representations of the equations are evaluated, and the residuals returned to the boundary value solver. 

The Chemkin package deals with problems that can be stated in terms of equation of state, thermodynamic properties, and chemical kinetics, but it does not consider the effects of fluid transport. Once fluid transport is introduced it is usually necessary to model diffusive fluxes of mass, momentum, and energy, which requires knowledge of transport coefficients such as viscosity, thermal conductivity, species diffusion coefficients, and thermal diffusion coefficients. Therefore, in a software package analogous to Chemkin, we provide the capabilities for evaluating these coefficients. ... 

Nemst, 1888). This eqnation is valid in dilnte solntions. An analogous equation including activity coefficients can be derived, bnt for the reasons outlined above, it again is not sufficiently accnrate in describing the experimental data in concentrated soluhons. Equahon (4.6) is of great valne becanse it can be nsed to evaluate ionic diffusion coefficients from valnes of Uj which are more readily measnred. 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

By varying the scan rate, this equation allows then the evaluation of the diffusion coefficient of the transferring ion. With the determination of the formal transfer potential of an ion and thus of its Gibbs energy of transfer by application of Eq. (10), this is the most important application of cyclic voltammetry. 

Experimental Methods to Evaluate Diffusion Coefficients and Investigate Transport Processes of Pharmaceutical Interest... 

Thus, the side-by-side device, when properly calibrated, is a versatile and useful method to determine diffusion coefficients, to evaluate mass transport mechanisms, and to evaluate up-to-date drug delivery systems. 

Koizumi and Higuchi [18] evaluated the mass transport of a solute from a water-in-oil emulsion to an aqueous phase through a membrane. Under conditions where the diffusion coefficient is expected to depend on concentration, the cumulative amount transported, Q, is predicted to follow the relationship... 

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