Fractionating factor

For example, if a carbonaceous sample (S) is examined mass spectrometrically, the ratio of abundances for the carbon isotopes C, in the sample is Rg. This ratio by itself is of little significance and needs to be related to a reference standard of some sort. The same isotope ratio measured for a reference sample is then R. The reference ratio also serves to check the performance of the mass spectrometer. If two ratios are measured, it is natural to assess them against each other as, for example, the sample versus the reference material. This assessment is defined by another ratio, a (the fractionation factor Figure 48.2). 

To quantify this change, a fractionation factor (a) is used where,... 

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). 

The difference in 5 values for two substances (P,Q) measured against a standard substance is approximately equal to 1000 times the natural logarithm of their fractionation factor (app). 

Instead of the fractionation factor (apQ) for two substances (P,Q), a slightly different fractional abundance (/pq) may be defined ... 

Isotope ratios are commonly reported as relative abundance (R), and comparison of two ratios (R, R2) represent the a-value (known as a fractionation factor). 

Fig. 6. Share of U.S. market occupied by human albumin/plasma protein fraction, (—) Factor VIII concentrate, (-) intravenous immunoglobulin...

Distillation. Vacuum distUlation (qv) of water, which contains the three molecular species H2O, HDO, and D2O, was the first method used for the large-scale extraction of deuterium (10,58) (Fig. 2). From the equHibrium constant in the Hquid phase it is evident that the distribution of H and D is not statistical. The differences in vapor pressure between H2O and D2O are significant, and a fractionation factor (see Table 7) of 1.05 can be obtained at... 

Distillation of Hquid hydrogen as a method for separating deuterium received early consideration (10,58) because of the excellent fractionation factor that can be attained and the relatively modest power requirements. The cryogenic temperatures, and the requirement that the necessarily large hydrogen feed be extremely pure (traces of air, carbon monoxide, etc, are soHds at Hquid hydrogen temperature) have been deterrents to the use of this process (see... 

That is, terms of the form (1 — jr -I- jr< )/) appear in the denominator for all reactant sites having exchangeable protons and similarly in the numerator for all transition state sites. If there is no change in the fractionation factor for a site, its contribution cancels. If the solvent is a reactant, its term disappears because the solvent fractionation factor is unity by definition. 

The fractionation factor toward D versus H for the species 1 is defined relative to that for the solvent s. Represented as , it is defined as... 

Bottinga, Y. 1969 Calculated fractionation factors for carbon and hydrogen isotope exchange in the system calcite-carbon dioxide-graphite-methane-hydrogen-water vapour. Geochimica et CosmochimicaActa 33 49-64. 

Wong, W.W., Cochran, W.J., Klish, W.J., Smith, E.O.B., Lee, L.S. and Klein, P.D. 1988 In vivo isotope-fractionation factors and the measurement of deuterium- and oxygen-18-dilution spaces from plasma, urine, saliva, respiratory water vapor, and carbon dioxide. American Journal of Clinical Nutrition 47 1-6. 

On the other hand, the scrambled model of carbon sourcing does not seem to be applicable when we consider the metabolic fate of fatty acids. We find that there are partial barriers to the movement of FA-derived carbon atoms into the synthesis of proteins. This partial restriction leads us to expect a trophic level effect in the fractionation between collagen and bone apatite or respired CO2 of which apatitic carbonate is a sample. The magnitude of the fractionation depends on two separate fractionation factors which cannot be disentangled by analyses of bone samples alone. 

Results have been expressed in a number of ways. In the Raleigh model that has been extensively used, the fractionation factor a is given by R/Rq = when the fraction of remaining substrate is/and where R is the isotopic composition of the substrate during degradation and Rq is the initial value. The enrichment factor e where e = 1000 (a - 1) has also been used. There are certain conditions that must be fulfilled for the Raleigh model to be applicable ... 

A comparison had been made of fractionation during the dechlorination of tetrachlo-roethene by Sulfurospirillum multivorans and Desulfitobacterium sp. strain PCE-S in laboratory experiments (Nijenhuis et al. 2005). Isotope fractionation in growing cultures was 1.0052 for Desulfitobacterium sp. and only 1.00042 for Sulfurospirillum multivorans, whereas fractionation was greater in crude cell extracts from both strains. It was concluded that caution should therefore be exercised in applying fractionation factors to the evaluation of in situ bioremediation. 

Isotope ratios for and Cl were measured for the aerobic degradation of dichlorometh-ane by a methanotroph MC8b (Heraty et al. 1999). Values of the fractionation factor (a) were 0.9586 for carbon and 0.9962 for chlorine, and kinetic isotope effects were 1.0424 for carbon and 1.0038 for chlorine. 

Three anaerobic dechlorinating consortia were used to examine fractionation during dechlorination of tetrachloroethene and TCE to cii-dichloroethene (Numata et al. 2002). Fractionation factors (a) for the first reaction ranged from 0.987 to 0.991 for the three consortia, and for the second reaction were 0.9944 for all consortia. Some important limitations were pointed out (a) the chlorinated ethenes were not separated so that the isotopic... 

Oxygen isotopic fractionation factors used for the calculation were taken from Taylor (1997). Initial 8 0 value of hydrothermal solution (0%o) was estimated from 8 0 values of K-feldspar and quartz in the veins and homogenization temperatures (Shikazono and Nagayama, 1993), and that of groundwater (—7%c) was estimated from meteoric water value of the south Kyushu district (—7%c) (Matsubaya et al., 1975). 

Friedman I, O Neil JR (1977) Compilation of stable isotope fractionation factors of geochemical interest. U S Geol Surv Prof Paper 440-KK... 

The differential removal of Th and Pa from the open ocean can be expressed in terms of a fractionation factor (Anderson et al. 1983b), F(Th/Pa), where ... 

Figure 8. Partition coefficients (Kd) for Th and Pa and the fractionation factor (F) between Th and Pa plotted as a function of the opal and calcium carbonate percentage in settling particulate material. Note the tendency for the Kd for Th to increase with increasing carbonate fraction and decrease with increasing opal fraction. Pa shows the opposite behavior so that F increases with low opal fraction or high carbonate fraction. This plot is modified from Chase et al. (in press-b) but excludes the continental margin data also shown in that study and instead focuses exclusively on open-ocean sites.

Figure 14.1 Stylised diagram illustrating the inputs and outputs that determine analyte isotope ratios. The analyte can be a compound, a position in a compound, or a bulk mixture. Inputs 1 and 2 and outputs 3 and 4 are internal to the system (e.g. an organism). Inputs 1A, 1B, 2A, and 2B are external contributors to inputs 1 and 2, respectively. The isotope ratios of inputs 1 and 2 depend on relative flux (e.g. diet) from the outside. axare fractionation factors between precursors and products. The isotope ratio of the analyte (RAnalyte) is a composite of the relative contributions of inputs I and 2 and degradation to outputs 3 and 4. Adapted from Brenna (2001)...

Besides the outer sphere electron transfers, we have identified (Albery, 1975d) another class of reactions that exhibit Case III behaviour, and this example is proton transfer to cyanocarbon bases. These reactions were studied by Long and co-workers. First, by using tritium, they measured the fractionation factor for the tritium as it was pulled off the carbon as in [1], The results... 

---