Experimental Measurements of Diffusivities

A slightly modified form of expression was obtained by Ash and Barrer who used a somewhat different definition of the transport diffusivity. If the cross coefficient can be neglected (I. wO), Eq. (5.9) reduces to Eq. (5.6) with Dq = S), which is the familiar Darken equation/ originally derived for the interdiffusion of two alloys. While Eq. (5.6), being essentially a definition of Dq, is always valid it is evident that the assumption that Dq- is only true in the limiting case where In general both Z)q and are 

For an activated zeolitic diffusion process, involving transition through a window between two cages, an expression of the same general form as Eq. (5.9) may be derived from simple microdynamic considerations if it is assumed that the interference effect represented by the cross coefficient in Eq. (5.7) arises from the periodic blocking of the window with a probability proportional to the counterdiffusing flux.  

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If the far exceeds the cylinder length, over which experimental measurements of diffusion distribution of EEPs are taken, then the EEP radiative term found in expression (5.10) may be neglected. If such an approximation cannot be done, then the rate constant of radiative decay should be taken into consideration in processing the experimental data. 

As an illustration of the current state of the art for electronic spectroscopy of transition metal ions in zeolites, refer to the recent review by Schoonheydt of Cu2+ in different zeolites [56]. Schoonheydt shows that experimental measurement of diffuse reflectance spectra (and in the case of Cu2 + EPR spectra) must be combined with theoretical calculations if a complete interpretation is to be made. The exact frequencies of the d-d transitions in the electronic spectrum of Cu2+ are independent of the zeolite structure type, the Si Al ratio, and the co-exchanged cations, but depend solely on the local coordination environment. Figure 20 shows the diffuse reflectance spectrum of dehydrated Cu-chabazite the expanded portion reveals the three d-d transitions in the region around 15000 cm l. 

Motivation for these definitions is often rooted in experimental measurement of diffusion coefficient (we try here to use the referential velocity which is zero in the measuring device movement of constituent relatively to it is just the diffusion). Usually, it is used (4.539) in gases, (4.540) in liquid, mixing of which is nearly ideal (4.440). 

The mechanisms of diffusion in these two systems (gas and liquid) are different and unrelated diffusion in gases is the result of the collision process, whereas that in liquids is an activated process (Bird et al., 1960). Diffusion in microp-orous materials is neither gaseous nor liquid diffusion. The closest case for such diffusion is surface diffusion, where molecules hop within the surface force field (see review by Kapoor et al., 1989b). Pick s law is used for both application (in modeling of adsorption processes) and experimental measurement of diffusion. Extensive reviews are available on diffusion in microporous materials and zeolites (Karger and Ruthven, 1992 Do, 1998). A lucid discussion on the nonlinear, and in some cases peculiar, phenomena in zeolite diffusion was given... 

To apply the above scheme, accurate experimental measurements for the transport properties of the monatomic fluids were collected. In Table 10.1 the experimental measurements of diffusion, viscosity and thermal conductivity used for the correlation scheme are shown. This table also includes a note of the experimental method used, the quoted accuracy, the temperature range, the maximum pressure and the number of data sets. The data cover the range of compressed gas and the liquid range but not the critical region, where there is an enhancement (Chapter 6) which cannot be accounted for in terms of this simple molecular model. 

EXPERIMENTAL MEASUREMENT OF DIFFUSION COEFFICIENTS CONCOMITANT WITH ADSORPTION... 

The process requires the interchange of atoms on the atomic lattice from a state where all sites of one type, e.g. the face centres, are occupied by one species, and the cube corner sites by the other species in a face-centred lattice. Since atomic re-aiTangement cannot occur by dhect place-exchange, vacant sites must play a role in the re-distribution, and die rate of the process is controlled by the self-diffusion coefficients. Experimental measurements of the... 

Despite the plethora of data in the scientific literature on thermophysical quantities of substances and mixtures, many important data gaps exist. Predictive capabilities have been developed for problems such as vapor-liquid equihbrium properties, gas-phase and—less accmately—liquid-phase diffusivities, aud solubilities of uouelectrolytes. Yet there are many areas where improved predictive models would be of great value. Au accrrrate and rehable predictive model can obviate the need for costly, extensive experimental measurements of properties that are critical in chemical manufactming processes. 

Experimental measurements of DH in a-Si H using SIMS were first performed by Carlson and Magee (1978). A sample is grown that contains a thin layer in which a small amount (=1-3 at. %) of the bonded hydrogen is replaced with deuterium. When annealed at elevated temperatures, the deuterium diffuses into the top and bottom layers and the deuterium profile is measured using SIMS. The diffusion coefficient is obtained by subtracting the control profile from the annealed profile and fitting the concentration values to the expression, valid for diffusion from a semiinfinite source into a semi-infinite half-plane (Crank, 1956),... 

Experimental measurements of surface diffusion are usually calculated by subtracting from the measured total diffusion that predicted theoretically for Knudsen and molecular diffusion. 

It is evident that (once the electrochemical reversibility of the process under examination has been checked, see the next section) the experimental measurement of the peak current, ip, allows one to calculate one of the parameters appearing in the equation. For instance, if the peak current ip at a certain scan rate v is measured, knowing the area of the electrode A, the diffusion coefficient D and the concentration C of the species under study, one can compute the number of electrons n involved in the redox change. On the other... 

Apparatus. Preliminary experiments were carried out in a modified Kiselev-type cell [21 ] with a grating spectrometer, PERKIN ELMER model 325. Precise measurements of diffusivities were conducted by means of a fast Fourier Transform IR (FTIR) spectrometer, PERKIN ELMER model 1800 inserted in a complex set-up equipped with UHV, gas dosing and mass flow control systems. Details of the cell and experimental devices will be described elsewhere [22]. 

For experimental determination of diffusion coefficients, a large database is already available. Nonetheless, data for specific applications are often difficult to find because the data may not cover the right temperature range, mineral compositions, or fluid conditions. In geospeedometry applications, data often must be extrapolated to much lower temperatures and the accuracy of such extrapolation is difficult to assess. Because the timescale of geological processes is often in the order of Myr, and that of experiments is at most years, instrumental methods to measure very short profile are the key for the determination of diffusion coefficients that are applicable to geologic problems. 

In comparison with the qualitative description of diffusion in a binary system as embodied by Eqs. (11), (12) or (14), the thermodynamic factors are now represented by the quantities a, b, c, and d and the dynamic factors by the phenomenological coefficients which are complex functions of the binary frictional coefficients. Experimental measurements of Dy in a ternary system, made on the basis of the knowledge of the concentration gradients of each component and by use of Eqs. (21) and (22), have been reviewed 35). Another method, which has been used recently36), requires the evaluation of py from thermodynamic measurements such as osmotic pressure and evaluation of all fy from diffusion measurements and substitution of these terms into Eqs. (23)—(26). 

An experimental measurement of the one-dimensional displacement distributions has been reported for self-diffusion of W on the W (112) plane by Ehrlich Fudda,86 and Re on W (112).134 Their result agrees with eq. (5.57) to within statistical uncertainties. However, a later result by Ehrlich135 agrees better with a model having 10% of the atomic jumps extended to the second nearest neighbor distance. 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

Stewart, P. S., A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms , Biotechn. Bioeng., 59,261-272 (1998). 

The calculations led to predictions of adsorption sites for the nonpolar compounds that are in good agreement with those determined experimentally. The cation site is preferred over the window site. The activation barrier for movement between two cation sites was calculated to be 30 kJ/ mol and that for movement between a cation and a window site 43 kJ/mol. Experimental measurements of activation barriers to diffusion of benzene in faujasites are between 17 and 27 kJ/mol (24). The calculations provide strong support for the mechanism of surface-mediated diffusion for all guest molecules in the limit of infinite dilution and 0 K. The MEPs show that molecules slide along the wall of the supercage, with the plane of the aromatic ring almost parallel to the pore wall. 

I.K. Puri, K. Seshadri, M.D. Smooke, and D.E. Keyes. A Comparison between Numerical Calculations and Experimental Measurements of the Structure of a Counterflow Methane-Air Diffusion Flame. Combust. Sci. Techn., 56 1-22,1987. 

The wavelength dependence in Eq. 14.13 can be used for experimental measurements of the surface and kinetic coefficients that constitute Bs. If an array of evenly spaced parallel grooves is introduced on a surface, the spacing dependence of the grooves amplitude-decay factor can be measured [6]. An analysis for flattening of an isotropic surface by bulk diffusion as in Fig. 3.7 is presented in Exercise 14.1. 

This study comprised the first reported direct experimental measurement of surface diffusion in air-suspended thin liquid films. 

The rate of diffusive separation, k, was determined from separate experimental measurements of iodine radical diffusion rates in the high pressure diffusion limited regime (19). The rate of excited state deactivation, k i, was calculated from the measured quantum yields at high densities where G> = kd/k i (18). It was assumed that k i is proportional to the inverse diffusion coefficient, D 1 (19,23) as both properties are related to the collision frequency. 

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