Isotope exchange principles

We have previously assumed that the principle diagenetic process is attributable to exchange or interaction of (depleted) browser apatite values with (enriched) sedimentary matrix values (Lee-Thorp and van der Merwe 1987). Another possibility is ionic or isotopic exchange with soil CO2 however in most cases soil CO2 values will be closely related to matrix carbonate values. If the former is the case, one would expect enriched grazer values (near 0%o)... 

In principle, the three isotope method may be widely applied to new isotope systems such as Mg, Ca, Cr, Fe, Zn, Se, and Mo. Unlike isotopic analysis of purified oxygen, however, isotopic analysis of metals that have been separated from complex matrices commonly involves measurement of several isotopic ratios to monitor potential isobars, evaluate the internal consistency of the data through comparison with mass-dependent fractionation relations (e.g., Eqn. 8 above), or use in double-spike corrections for instrumental mass bias (Chapter 4 Albarede and Beard 2004). For experimental data that reflect partial isotopic exchange, their isotopic compositions will not lie along a mass-dependent fractionation line, but will instead lie along a line at high angle to a mass-dependent relation (Fig. 10), which will limit the use of multiple isotopic ratios for isobar corrections, data quality checks, and double-spike corrections. 

Criss RE (1999) Principles of Stable Isotope Distribution. Oxford Univ Press, New York Criss RE, Gregory RT, Taylor HP (1987) Kinetic theory of oxygen isotope exchange between minerals and water. Geochim Cosmochim Acta 51 1099-1108... 

For geologic purposes, the dependence of the equilibrium constant K on temperature is the most important property (4). In principle, isotope fractionation factors for isotope exchange reactions are also slightly pressure-dependent because isotopic substitution makes a minute change in the molar volume of solids and liquids. Experimental studies up to 20kbar by Clayton et al. (1975) have shown that the pressure dependence for oxygen is, however, less than the limit of analytical detection. Thus, as far as it is known today, the pressure dependence seems with the exception of hydrogen to be of no importance for crustal and upper mantle environments (but see Polyakov and Kharlashina 1994). 

Deuterium labelling can, in principle, provide mechanistic information on hydro-formylation reactions, but complications may arise if scrambling of the D-label bet veen a metal hydride and D2 is fast. The isotopic exchange reaction shown in Eq. (9) was probed by rapid scan HP IR spectroscopy (1.3 scans s" ) where 21 is the bidentate pyrrolyl-based phosphorus amidite ligand illustrated [8]. 

Dual Temperature Process. A unit of a dual temperature cascade is shown schematically in Figure 8. The dual temperature system operates on the principle that isotope exchange reactions, like all chemical reactions, change their equilibrium constants with temperature. The general, but far from universal (22), rule is that in systems with large isotopic... 

The equilibrium constant K for an isotopic exchange reaction depends on the vibrational frequency shifts produced upon isotopic substitution and can be calculated in principle from knowledge of the fundamental frequencies of the isotopic species. At high temperatures differences in chemical properties cease. 

According to the underlying principle, the methods are grouped into spectroscopic, thermal and calorimetric, adsorption and wetting, isotopic exchange, microscopic, scattering, and chemical reactions techniques (Table II) (14-29), This chapter is not a comprehensive treatment of all methods in depth. Results of spectroscopic and adsorption methods are discussed for aspects of content of information, validity, applicability, and limitations. 

In principle, the free energy change and in turn the equilibrium constant for such reactions can be calculated from conventional thermodynamic data (molar enthalpy, entropy, volume data) on the end-member isotopic species denoted in the reaction. This approach, however, is generally not practicable because of the paucity of thermodynamic data on isotopically pure end-members. Moreover, even if such data were widely available, the Gibbs free energy changes associated with most isotope exchange reactions... 

For geochemical purposes, the dependence of isotope fractionation factors on temperature is the most important property. In principle, fractionation factors for isotope exchange reactions are also slightly pressure-dependent, but experimental studies have shown the pressure dependence to be of no importance within the outer earth environments (Hoefs 2004). Occasionally, the fractionation factors can be calculated by means of partition functions derivable from statistical mechanics. However, the interpretation of observed variations of the isotope distribution in nature is largely empirical and relies on observations in natural environments or experimental results obtained in laboratory studies. A brief summary of the theory of isotope exchange reactions is given by Hoefs (2004). 

A method that is potentially very powerful in distinguishing between various candidate mechanisms for an enzyme is that of isotope exchange at equilibrium [68-70], It has been relatively little used, although the principle is elegant, because it is experimentally tedious each piece of information represents many laborious measurements. The principle may be easily illustrated by considering Schemes 8 and... 

Although r-benzenechromium tricarbonyl, 3r-C6HeCr(CO)3, is one of the best characterized arenechromium tricarbonyls, other arenes also form complexes with Cr(CO) 3. Accordingly, although isotopic exchange apparently has been investigated only with jr-benzenechromium tricarbonyl, and its simple derivatives in principle the method may be generally applicable to polycyclics. 

Isotope exchange diffusion profiles can also be measured ex situ by SIMS, and can, in principle, reveal surface kinetics in addition to bulk transport... 

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