Isotope labeling diffusion

Let us consider another situation where a force (or forces) is not compensated on a time average. Then the particles upon which the force is exerted become transported in the medium. This translocation phenomenon changes with time. Particle transport, of course, also occurs under equilibrium conditions in homogeneous media. Self-diffusion is a process that can be observed and its velocity can be measured, provided that a gradient of isotopically labelled species is formed in the system at constant composition. 

In animal studies [9], up to 8% of isotopically labelled mercuric chloride applied to the skin was absorbed within 5 h. The state of the skin is one factor which determines the rate of absorption [10]. Passive diffusion cannot be the only process involved, since the absolute absorption rate of mercury increases with increasing concentration up to a plateau value. In addition, skin absorption probably occurs transepidermally rather than via the follicular pathway [11]. 

It is important to note that even in the presence of sufficient proton density and in the case of differential isotope labeling, efficient spin-diffusion may complicate the interpretation of the NOE data and result in structures or relative orientations that are erroneous. A similar problem does not occur when using residual dipolar couplings. 

The diffusion of alkyl ammonium ions into clay pellets has been studied by bringing the pellet into superficial contact with an isotopically labeled salt and then, after a suitable time, using a microtome to slice the pellet. The radioactivity is then measured in successive thin slices of the pellet. Assuming that Equation (62) describes the diffusion process, estimate how long it would take for 1% of the initial activity of each of the ions to appear in the 15th slice inward from the exposed surface of the dry clay if each slice is 40-pm thick. The diffusion coefficients for the methyl and trimethyl ammonium cations under these conditions are 7.03 x 10-12 and 2.65 x 10 " cm2 s, respectively.f... 

Self diffusion coefficients can be obtained from the rate of diffusion of isotopically labeled solvent molecules as well as from nuclear magnetic resonance band widths. The self-diffusion coefficient of water at 25°C is D= 2.27 x 10-5 cm2 s 1, and that of heavy water, D20, is 1.87 x 10-5 cm2 s 1. Values for many solvents at 25 °C, in 10-5 cm2 s 1, are shown in Table 3.9. The diffusion coefficient for all solvents depends strongly on the temperature, similarly to the viscosity, following an Arrhenius-type expression D=Ad exp( AEq/RT). In fact, for solvents that can be described as being globular (see above), the Stokes-Einstein expression holds ... 

The Fick s law diffusion coefficient of a permeating molecule is a measure of the frequency with which the molecule moves and the size of each movement. Therefore, the magnitude of the diffusion coefficient is governed by the restraining forces of the medium on the diffusing species. Isotopically labeled carbon in a diamond lattice has a very small diffusion coefficient. The carbon atoms of diamond move infrequently, and each movement is very small—only 1 to 2 A. On the other hand, isotopically labeled carbon dioxide in a gas has an extremely large diffusion coefficient. The gas molecules are in constant motion and each jump is of the order of 1000 A or more. Table 2.1 lists some representative values of diffusion coefficients in different media. 

Isotopic labeling of the Cp rings enables the study of selfexchange reactions using the ICR technique. The rate constants for the gas-phase reactions are close to the diffusion limit and about 10" times larger than their solution phase equivalents. The slower solution reactions correspond to Xs (12 to 13) xlO cm. ... 

The ZLC method offers advantages of speed and simplicity and requires only a very small adsorbent sample thus making it useful for characterization of new materials. The basic experiment using an inert carrier (usually He) measures the limiting transport difiiisivity (Do) at low concentration. A variant of the technique using isotopically labeled tracers (TZLC) yields the tracer diffiisivity and counter diffusion in a binary system may also be studied by this method. To obtain reliable results a number of preliminary experiments are needed, e.g. varying sample quality, nature of the purge gas, the flow rate and, if possible, particle size to confirm intracrystalline diffusion control. 

Here Ca is the concentration of isotopically labelled species at a point where the concentration of unlabelled species is Ca. La a and La a are the straight and cross phenomenological coefficients of the irreversible thermodynamic formulation of diffusion. The original relation, Equation 1, assumes a zero cross coefficient, which in dense intracrystalline fluids certainly is not likely to be true. 

Isotope labeling experiments have shown chlorite to be the sole source of the oxygen atoms in the O2 product.30 EPR and UV-Vis studies also suggest that Cld forms a compound I-like intermediate upon reaction with CIO2. However, the hypochlorite (CIO ) by-product is believed to not diffuse freely into solution, but instead remains protein bound for further reaction with the ferryl to afford 02. The mechanism illustrated in Figure 3.8 has been put forth for this unique heme enzyme. 

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