Kinetics fractional

Macko, S.A., Estep, M.L.E., Engel, M.H. and Hare, RE. 1986 Kinetic fractionation of stable nitrogen isotopes during amino acid transamination. Geochimica et Cosmochimica Acta 50 2143-2146. 

Figure 9.16 Kinetic fractionation during crystal growth. Steady-state distribution of melt concentrations in the vicinity of a solid growing at the rate v for trace elements with different solid-liquid fractionation coefficients [equation (9.6.5), Tiller et al. (1953)]. The stippled area indicates the steady-state chemical boundary-layer with thickness <5 = <5>/v.

Most sorption/desorption kinetic models fit the data better by including an instantaneous, non-kinetic fraction described by an equilibrium sorption constant. 

Equations (8) and (10) are applicable to stable isotope systems where isotopic fractionation occurs through mass-dependent processes which comprise the majority of cases described in this volume. These relations may also be used to identify mass-independent fractionation processes, as discussed in Chapter 2 (Birck 2004). Mass-dependent fractionation laws other than those given above distinguish equilibrium from kinetic fractionation effects, and these are discussed in detail in Chapters 3 and 6 (Schauble 2004 Yormg and Galy 2004). Note that distinction between different mass-dependent fractionation laws will generally require very... 

Turner JV (1982) Kinetic fractionation of carbon-13 during calcium carbonate precipitation. Geochim... 

Kinetic fractionations can occur when there is incomplete isotopic exchange between the different phases present in a system. A thorough introduction to kinetic stable isotope fractionation theory is unfortunately beyond the scope of the present review. Flowever, it is useful to include a brief discussion of some basic aspects, particularly in comparison to equilibrium fractionation theory. A simple example of kinetic fractionation is the evaporation of a liquid water droplet into a vacuum, in this example FljO molecules entering the gas phase are physically removed from the vicinity of the droplet, so there is no chance for isotopic equilibration between vapor-phase molecules and the residual liquid. Isotopic fractionation in this case is determined by a one-way reaction path, and will not, in general, be the same as the fractionation in a system where vapor-phase molecules are able to equilibrate and exchange with the liquid. In other reactions, isotopic exchange is limited by an energy barrier—an... 

Figure 7. Using a theoretically determined equilibrium fractionation to interpret measured isotopic fractionations in a hypothetical mineral-solution system. Three sets of data are shown. The theoretical equilibrium fractionation for this system is indicated by the gray arrow. The first set of data, indicated by circles, closely follow the calculated fractionation, suggesting a batch equilibrium fractionation mechanism. The second set of data (stars) is displaced from the theoretical curve. This may either indicate a temperature-independent kinetic fractionation superimposed on an equilibrium-like fractionation, or that the theoretical calculation is somewhat inaccurate. The third set of data (crosses) shows much greater temperature sensitivity than the equilibrium calculation this provides evidence for a dominantly non-equilibrium fractionation mechanism. For the first data set, the theoretical fractionation curve can be used to extrapolate beyond the measured temperature range. The second data set can also be extrapolated along a scaled theoretical curve (Clayton and Kieffer 1991).

For translational kinetic fractionations dependent on molecular velocities, a slightly different relation holds (Young et al. 2002),... 

The masses in the kinetic P will be reduced masses if the rate limiting step involves vibrations (as during bond rupture), they will be molecular masses of isotopomers if the kinetic process involves transport of molecules, and they will be atomic masses if transport of atoms is involved. The value of the kinetic P goes down as the masses in (12) increase. As a result, an estimate of the maximum value for p during the kinetic fractionation of Mg isotopes is obtained by equating the M, values with the atomic masses of Mg. The kinetic P obtained from the atomic masses of Mg is 0.5110. 

Figure 7. A Mg vs. 5 Mg plot of calcite speleothems and their drip waters from the Soreq cave site, Israel (data from Galy et al. 2002) compared with seawater. The horizontal trend of the data suggests that Mg in carbonates is related to aqueous Mg by equilibrium fractionation processes. Results of a three-isotope regression, shown on the figure and in Table 3, confirm that the (3 value defined by the data is similar to the predicted equilibrium value of 0.521 and distinct from kinetic values. The positive A Mg characteristic of the speleothem carbonates is apparently inherited from the waters. The positive A Mg values of the waters appear to be produced by kinetic fractionation relative to primitive terrestrial Mg reservoirs (the origin).

Figure 8. A Mg vs. 5 Mg plot of limestone, dolostone, and marble samples (data from Galy et al. 2002) compared with a sample of foraminifera of various species (Chang et al. 2003) and seawater (Chang et al. 2003, this study). The broadly horizontal trend of the carbonates at elevated A Mg suggests a component of equilibrium fractionation relative to seawater. The P value derived by regression of these 5 Mg and 5 Mg data is within the range for equilibrium fractionation and statistically distinguishable from purely kinetic fractionation.

Mg that is likely to he fractionated hy kinetic processes relative to primitive terrestrial Mg reservoirs (the origin), follow a kinetic fractionation path relative to the origin. The P value derived hy regression of these 6 Mg and 6 Mg datais statistically indistinguishable from the kinetic value of 0.511 and clearly resolved from the equilibrium value of 0.521. 

The high precision with which Mg isotope ratios can be measured using MC-ICPMS opens up new opportunities for using Mg as a tracer in both terrestrial and extraterrestrial materials. A key advance is the ability to resolve kinetic from equilibrium mass-dependent fractionation processes. From these new data it appears that Mg in waters is related to mantle and crustal reservoirs of Mg by kinetic fractionation while Mg in carbonates is related in turn to the waters by equilibrium processes. Resolution of different fractionation laws is only possible for measurements of Mg in solution at present laser ablation combined with MC-ICPMS (LA-MC-ICPMS) is not yet sufficiently precise to measure different fractionation laws. 

Although most of the studies reviewed here involve kinetic isotope effects, estimates of equilibrium fractionations are useful in obtaining an understanding of potential isotopic fractionations between species and insight into bonding issues without the added complications inherent in kinetic fractionations. Krouse and Thode (1962) used measured vibrational spectra... 

Composite effects of equilibrium and kinetic fractionations in an experiment... 

Although equilibrium fractionations have been documented for some transition metal (i.e., Fe), they should be small and may be overwhelmed by kinetic fractionations in low-temperature and biological systems (Schauble 2004). For any transition metal, it remains to be demonstrated that biological effects dominate the natural isotope variability. 

As is well known the isotopic composition of water is controlled by two mass-dependent processes (1) the equilibrium fractionation that is caused by the different vapor pressures of H2 0 and H2 0 and (2) the kinetic fractionation that is caused by the different diffusivities of H2 0 and H2 0 during transport in air. Angert et al. (2004) have demonstrated that for kinetic water transport in air, the slope in a 5 0-5 0 diagram is 0.511, whereas it is 0.526 for equilibrium effects. Similar values have been given by Luz and Barkan (2007). is thus a unique tracer, which is, in contrast to the deuterium excess, temperature-independent and which may give additional information on humidity relations. 

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