Diffusion coefficients determination

Hence, from equation (10.48), the effective diffusion coefficient determined by "chromatographic" testing is given by... 

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. 

Experimental methods for determining diffusion coefficients are described in the following section. The diffusion coefficients of the individual ions at infinite dilution can be calculated from the ionic conductivities by using Eqs (2.3.22), (2.4.2) and (2.4.3). The individual diffusion coefficients of the ions in the presence of an excess of indifferent electrolyte are usually found by electrochemical methods such as polarography or chronopotentiometry (see Section 5.4). Examples of diffusion coefficients determined in this way are listed in Table 2.4. Table 2.5 gives examples of the diffusion coefficients of various salts in aqueous solutions in dependence on the concentration. 

Capillaries and tubes (free boundary method) Diffusion coefficient determination 1,2... 

Side-by-side diffusion cell (membrane method) Diffusion coefficient determination mass transport studies 10-14... 

A Goldberg, W Higuchi. Improved method for diffusion coefficient determinations employing the silver membrane filter. J Pharm Sci 57 1583, 1968. 

This method is commonly used to obtain the diffusion coefficient through porous membranes. The schematic diagram illustrating the best technique for application of the time-lag method for determination of diffusion transport is shown in Fig. 4. As in the test setup shown in Fig. 4 a, the soil is contained between the source and collection reservoirs. Using this technique for diffusion coefficient determination of pollutants requires that the following conditions are satisfied ... 

The root time method of data analysis for diffusion coefficient determination was developed by Mohamed and Yong [142] and Mohamed et al. [153]. The procedure used for computing the diffusion coefficient utilizes the analytical solution of the differential equation of solute transport in soil-solids (i.e., the diffusion-dispersion equation) ... 

Selected entries from Methods in Enzymology [vol, page(s)] Analysis of GTP-binding/GTPase cycle of G protein, 237, 411-412 applications, 240, 216-217, 247 246, 301-302 [diffusion rates, 246, 303 distance of closest approach, 246, 303 DNA (Holliday junctions, 246, 325-326 hybridization, 246, 324 structure, 246, 322-324) dye development, 246, 303, 328 reaction kinetics, 246, 18, 302-303, 322] computer programs for testing, 240, 243-247 conformational distribution determination, 240, 247-253 decay evaluation [donor fluorescence decay, 240, 230-234, 249-250, 252 exponential approximation of exact theoretical decay, 240, 222-229 linked systems, 240, 234-237, 249-253 randomly distributed fluorophores, 240, 237-243] diffusion coefficient determination, 240, 248, 250-251 diffusion-enhanced FRET, 246, 326-328 distance measurement [accuracy, 246, 330 effect of dye orientation, 246, 305, 312-313 limitations, 246,... 

An intriguing aspect of these measurements is that the values of D determined from NMR and from sorption kinetics differ by several orders of magnitude. For example, for methane on (Ca,Na)-A the value of the diffusion coefficient determined by NMR is 2 x 10 5 cm2 sec-, and the value determined for sorption rates only 5 x 10"10 cm2 sec-1. The values from NMR are always larger and are similar to those measured in bulk liquids. The discrepancy, which is, of course, far greater than the uncertainty of either method, remained unexplained for several years, until careful studies (267,295,296) showed that the actual sorption rates are not determined by intracrystalline diffusion, but by diffusion outside the zeolite particles, by surface barriers, and/or by the rate of dissipation of the heat of sorption. NMR-derived results are therefore vindicated. Large diffusion coefficients (of the order of 10-6 cm2 sec-1) can be reliably measured by sorption kinetics... 

The question about the difference between the macroscopic and microscopic values of the quantities characterizing the translational mobility (viscosity tj, diffusion coefficient D, etc.) has often been discussed in the literature. Numerous data on the kinetics of spin exchange testify to the fact that, with the comparable sizes of various molecules of which the liquid is composed, the microscopic translational mobility of these molecules is satisfactorily described by the simple Einstein-Stokes diffusion model with the diffusion coefficient determined by the formula... 

All the proposed expressions require the knowledge of the diffusion coefficients. The binary diffusion coefficient determination is non trivial and it is usually made experimentally. 

A distinction between homodyne and heterodyne detection must be made in optical scattering and diffraction experiments. Without careful treatment of the background, there is always the risk of mixed or unknown coherence conditions, and the diffusion coefficient determined from such data may be off by a factor of two. At least for the signal and background levels present in TDFRS, heterodyne detection is always superior to homodyne, especially since the heterodyne signal, contrary to the homodyne one, turns out to be very stable against perturbations and systematic errors. Even under nearly perfect homodyne conditions the tail of the decay curve is almost unavoidably heterodyne [34]. 

This process is a relatively fast one and the diffusion coefficient determined from the correlation time of the fluctuations in the scattering can be too large202) giving too small radii, tm- To avoid this effect, Mazer et al.33) made measurements on sodium dodecyl sulphate in high salt concentration to contract the counterion charge cloud. 

Calculation and results. For each temperature we calculated the HMX molecular center-of-mass self-diffusion coefficient determined as ... 

The F uptake of flint takes a much longer time than that for bone. Fluorine diffusion into the depth of flint material is controlled by defect clusters. The diffusion coefficient determined by implanting a model compound (amorphous silica bombarded with heavy ions and hydrated at 100°C) is 9.10—21 cm2/s at room temperature. The corresponding penetration depth of F under ambient conditions in a 1000-year-old artefact can be estimated via x — (Dt)1/2 = 0.17. im [50], Thus, F accumulates only in the first micrometre of the surface. The surface of ancient flint artefacts can be altered by dissolution. The occurrence of this phenomenon is especially important in basic media. However, in some cases, the thickness of the dissolved layer can be neglected compared to the F penetration depth at low temperatures. Therefore, Walter et al. [35] proposed relative dating of chipped flint by measuring the full width at half maximum (FWHM) of F diffusion profiles in theses cases. 

The ApBq and A Bn layers are seen to grow parabolically, whereas the thickness of the ArBs layer will gradually decrease with passing time. Eventually, this layer will disappear. It is easy to notice that in this case the values of the diffusional constants k[A2 and kim can readily be determined from the experimental dependences x2- t and z2- t, respectively, using an artificially prepared specimen A-ApBq-ArBs-A iB,-B or A-A,B-B. It is essential to mention that both the ApBq and AtBn layers must be the first to occur at the A-B interface. The diffusional constant k[A2 thus obtained is the reaction-diffusion coefficient of the A atoms in the ApBq lattice, while the diffusional constant klB3 is the reaction-diffusion coefficient of the B atoms in the Afin lattice, to be compared with respective self-diffusion coefficients determined using radioactive tracers. 

Dg.c. diffusion coefficient determined from inverse gas chromatography... 

Table 4 contains a collection of diffusion coefficients determined experimentally for a variety of adsorbate systems. It shows that the values may vary considerably, which is of course due to the specific bonding of the adsorbate to the surface under consideration. Surface diffusion plays a vital role in surface chemical reactions because it is one factor that determines the rates of the reactions. Those reactions with diffusion as the rate-determining step are called diffusion-limited reactions. The above-mentioned photoelectron emission microscope is an interesting tool to effectively study diffusion processes under reaction conditions [158], In the world of real catalysts, diffusion may be vital because the porous structure of the catalyst particle may impose stringent conditions on molecular diffusivities, which in turn leads to massive consequences for reaction yields. 

Diffusion can also be used as a driving force in SPLITT channels. If one uses a SPLITT channel analogous to a gravitational-SPLITT-FFF channel where the sample is injected into inlet a (Fig. 26), the higher diffusion of smaller molecules allows them to cross the outlet splitting plane and thus to exit the lower outlet b, whereas larger molecules have a lower diffusion coefficient and exit from the upper outlet a. This method has been applied for continuous separations and diffusion coefficient determinations of a number of proteins [343,344]. 

A. Comparison of Self-Diffusion Coefficients Determined by Pulsed-Field Gradient NMR and Quasi-elastic Neutron Scattering... 

Fig. S. Comparison of the true Henry s law mode diffusion co licfent, Di> with the diffusion coefficient determined from time lag measurements at low nessure...

FIGURE 34.22 (a) Average interdiffusion coefficient values based on Run 1, (b) self-diffusion coefficient determination for Al -H pair... 

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