Diffusion, isotope factor

The earliest attempts to measure the rate of exchange between ferrous and ferric ions in aqueous media utilised the diffusion separation technique. Little agreement was obtained by the different workers Diffusion separation factors, found to be 0.5 , 1.4, 3.5 and 1.2, illustrate the difficulty of the technique. The isotopes used to label the iron were either Fe or Fe, and exchange was found to be complete in hours or many days > in perchlorate media. 

Enrichment is said to be mass dependent when it can be directly related to the difference in mass, as in the cases of evaporation and diffusion. The isotopic composition of a sample is characterised by the value 8 = Ri/Rstd — 1/ where Ri is the isotope ratio e.g. [ C]/[ C] in the sample and Rstd—a reference standard respectively. In a sample of N2O the enrichment will be mass dependent if the three-isotope factor p = = 0.51 (c/. Ref. [1]). In atmospheric nitrous... 

In liquid salts the isotope factor is in principle measurable by electrotransport (electromigration). Since many such measurements are available (13), it is especially tempting to study thermotransport in molten ionic media. One must bear in mind, however, the possibility of the following complications (a) the mechanisms of electrotransport, thermotransport, and self-diffusion may be non-identical see Reference 16) b) the isotope factors, as determined by electrotransport, are dependent, via transport numbers, on the reference system and (c) severe experimental difficulties may be encountered in liquid salt thermotransport, mainly corrosion and convection effects. 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

It should be noted that the separation factor for the centrifuge process is a function of the difference in the mol wts of the components being separated rather than, as is the case in gaseous diffusion, a function of their ratio. The gas centrifuge process would therefore be expected to be relatively more suitable for the separation of heavy molecules. As an example of the equiUbrium separation factor of a gas centrifuge, consider the Zippe centrifuge, operating at 60°C with a peripheral velocity of 350 m/s. From equation 68, OC is calculated to be 1.0686 for uranium isotopes in the form of UF. ... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

For a comparison of experimental Mossbauer isomer shifts, the values have to be referenced to a common standard. According to (4.23), the results of a measurement depend on the type of source material, for example, Co diffused into rhodium, palladium, platinum, or other metals. For Fe Mossbauer spectroscopy, the spectrometer is usually calibrated by using the known absorption spectrum of metallic iron (a-phase). Therefore, Fe isomer shifts are commonly reported relative to the centroid of the magnetically split spectrum of a-iron (Sect. 3.1.3). Conversion factors for sodium nitroprusside dihydrate, Na2[Fe(CN)5N0]-2H20, or sodium ferrocyanide, Na4[Fe(CN)]6, which have also been used as reference materials, are found in Table 3.1. Reference materials for other isotopes are given in Table 1.3 of [18] in Chap. 1. 

Four observation were thought to be in disagreement with the diffusion model (1) the lack of a proportional relationship between the electron scavenging product and the decrease of H2 yield (2) the lack of significant acid effect on the molecular yield of H2 (3) the relative independence from pH of the isotope separation factor for H2 yield and (4) the fact that with certain solutes the scavenging curves for H2 are about the same for neutral and acid solutions. Schwarz s reconciliation follows. 

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]. 

A good example of translational fractionation is one-way diffusion through an orifice that is smaller than the mean-free path of the gas. Related, but somewhat more complex velocity-dependent fractionations occur during diffusion through a host gas, liquid, or solid. In these fractionations the isotopic masses in the translational fractionation factor are often replaced by some kind of effective reduced mass. For instance, in diffusion of a trace gas JiR through a medium, Y, consisting of molecules with mass ttiy. 

Figure 7. Mo concentotions (o) and isotopic compositions ( ) from reducing pore fluids in Santa Monica Basin (McManus et al. 2002). Dotted line indicates seawater values for both variables. The data can be fit by a 1-D reaction-diffusion model wifli a fractionation factor of —1.005. The effective fractionation factor for Mo removal across tiie sediment-water interface is smaller, <1.0025 (see text).

An important consequence of such a model is that the effect of such sedimentary systems on the ocean Mo isotope budget is not represented by a, but rather by the relative fluxes of the isotopes across the sediment-water interface. This effective fractionation factor, is likely to be smaller than a (Bender 1990 Braudes and Devol 1997) because the diffusive zone acts as a barrier to isotope exchange with overlying waters, approximating a closed system. 

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