Fractionation factors, variations

To emphasize small variations in fractionation factors (a), a new term (5) is introduced, which accentuates small differences. Since the latter are very small, they are usually multiplied by 1000 (mil). 

As a rule, isotopes fractionate more strongly at low temperatures than they do at high temperature. Variation of the fractionation factor with absolute temperature 7k can be fit to a polynomial, such as,... 

In the earliest work, Krouse and Thode (1962) found the Se isotope fractionation factor Sse(iv)-se(o) to bc 10%o ( l%o) with hydroxylamine (NH2OH) as the reductant. Rees and Thode (1966) obtained a larger value, 12.8%o, for reduction by ascorbic acid. Webster (1972) later obtained 10%o for NHjOH reduction. Rashid and Krouse (1985) completed a more detailed study, and found that the fractionation factor varied with time over the course of the experiments. They explained the variations observed among the experiments in all four studies using a model in which reduction consists of two steps. With the rate constant of the second step two orders of magnitude smaller than the first, and kinetic isotope effects of 4.8%o and 13.2%o for the hrst and second steps, respectively, all the data (Table 3) were fit. Thus, kinetic isotope effects of apparently simple abiotic reactions can depend on reaction conditions. 

Fig. 10 Possible variation of isotopic fractionation factors with bond strength for hydrogen-bonded species. A,AH".

A further advancement comes from inter-laboratory comparison of two standards having different isotopic composition that can be used for a normalization procedure correcting for all proportional errors due to mass spechomehy and to sample preparation. Ideally, the two standard samples should have isotope raUos as different as possible, but still within the range of natural variations. There are, however, some problems connected with data normalization, which are still under debate. For example, the CO2 equilibration of waters and the acid extraction of CO2 from carbonates are indirect analytical procedures, involving temperature-dependent fractionation factors (whose values are not beyond experimental uncertainties) with respect to the original samples and which might be re-evaluated on the normalized scale. 

Natural isotope variations in chlorine isotope ratios might be expected due to both the mass difference between Cl and Cl as well as to variations in coordination of chlorine in the vapor, aqueous and solid phases. Schauble et al. (2003) calculated equilibrium fractionation factors for some geochemically important species. They showed that the magnitude of fractionations systematically varies with the oxidation state of Cl, but also depends on the oxidation state of elements to which Cl is bound with greater fractionations for 2+ cations than for 1+ cations. Silicates are predicted to be enriched compared to coexisting brines and organic molecules are enriched to dissolved Cl. ... 

Why are these equations represented by 4th order polynomials and not 2nd order curves given that the vertical variation of temperature and vapor fraction are well approximated by second order functions The simple answer is that the transition from condensing water vapor to liquid water above 0 °C to condensing water ice below -20 °C, and the attendant affect on the fractionation factor (Fig. 2), results in additional structure not captured by 2nd or 3rd order curves. Each of the equations fit their respective model output with an R2 > 0.9997. The lack of symmetry of the modeled uncertainty reflects asymmetry in the probability density function and particularly the long tail toward lower values of T relative to the mean (see Fig. 2 of Rowley et al. 2001). The effect of this long tail is well displayed in both Figure 5 and 7. 

It is interesting that for the different compounds in Table 21 AE/R has roughly the same value. We have also included the values for the solvent isotope effect for the solvolysis of isopropyl bromide. Heppolette and Robertson (1961) made an extensive study of the temperature variation of the solvent isotope effect for this compound. It can be seen that the values for isopropyl bromide match those of the other bromo compounds. The data for isopropyl bromide correlate well with the relative fluidities of HzO and D20 (Heppolette and Robertson, 1961) but this may arise because the AE/R values for the solvent isotope effect and for the relative fluidities happen by chance to be roughly equal. What is clear is that changing the group R has very little effect on the solvent isotope effect once one has allowed for the different temperatures at which the reactions are measured. This means that the solvent isotope effect for the solvolysis of halides is caused either by the LzO sites on the nucleophile having much the same fractionation factors or by the dynamic medium effect or by a combination of both. 

Equation (96) now expresses the medium-dependence of the fractionation factor cj>LX (or K95). However, we note that the quotient of activity coefficients contains ratios of the form J/ha/2(da which really represent isotope effects on transfer activity coefficients. For this reason, the activity coefficient quotient in equation (96) is expected to vary less rapidly with the isotopic composition of the solvent than the factor Y. Furthermore as a practical step, the inclusion of the variation of fractionation factors due to the transfer effect is an unrealistic refinement at the present time. 

Thus, the fractionation of boron isotopes between boron trifluoride and its molecular addition compounds may be explained in terms of unique characteristics of the boron and fluorine atoms. The model presented here adequately describes the direction of enrichment as well as the magnitude of the equilibrium constant. It accounts for observed variations in the size of fractionation factor for different donors as well as for different substituents on the same donor. The model correctly predicts the isotopic behavior of other boron halides when these are substituted for BF3 in the exchange reaction. Finally, the proposed model provides insight into the design of a practical chemical exchange system for the separation of boron isotopes. 

Variations in isotope ratios are not large so the fractionation factor a does not differ much... 

Schematic diagram of the stable nitrogen isotope ratios of different nitrogen reservoirs in the sea. The general range of stable isotope ratios (with respect to the atmosphere) found in nature is given in the boxes and the difference fractionation factors e (in %o) accompany arrows between the boxes. Many of the values are approximations because of the wide variations of observations. See Table 5.3 for more details of some of the reactions and the text for explanation. Values are based on data presented by Altabet and Small (1990), Altabet and Francois (1994) and Sigman and Casciotti (2001).

---