Isotope fractionation, chemical

Bigeleisen, J. and Ishida, T. Application of finite orthogonal polynomials to the thermal functions of harmonic oscillators. I. Reduced partition function of isotopic molecules, J. Chem. Phys. 48, 1311 (1968). Ishida, T., Spindel, W. and Bigeleisen, J. Theoretical analysis of chemical isotope fractionation by orthogonal polynomial methods, in Spindel, W., ed. Isotope Effects on Chemical Processes. Adv. Chem. Ser. 89, 192 (1969). 

Theoretical Analysis of Chemical Isotope Fractionation by Orthogonal Polynomial Methods... 

The differences in the properties of the isotopes of an element are called isotopic effect. The origin of an isotopic effect is always a physical phenomenon which can be attributed to the isotopic masses in chemical isotopic fractionations For example. 

Thus the reduced partition function ratio, (s/s )f, Is just the chemical Isotope fractionation factor of the chemical species against the gaseous atom. With the convention prime Is the light Isotope It Is easy to prove that ln(s/s )f Is always positive. This follows from the fact that u. > u.. 

Krueger, H.W. and Sullivan, C.H. 1984 Models for carbon isotope fractionation between diet and bone. In Tumland, J.R. and Johnson, P.E., eds.. Stable Isotopes in Nutrition. Washington D.C, American Chemical Society Symposium Series, No. 258 205-220. 

Grossman, E. and Ku, T.-L. 1986 Oxygen and carbon isotope fractionation in biogenic aragonite temperature effects. Chemical Geology (Isotope Geoscience Section) 59 59-74. 

Macko, S.A., Fogel, M.L., Hare, P.E. and Hoering, T.C. 1987 Isotopic fractionation ofnitrogen and carbon in the synthesis of amino acids by microorganisms. Chemical Geology (Isotope Geoscience Section) 65 79-92. 

Note that the chemical dimensions do not yield such robust "markers", or tracers, as the isotopic dimensions. For a given combustion source, for example, one is apt to find chemical--but not isotopic—fractionation varying significantly with time, particle size, particle history (differential volatilization or reaction), etc. The ratio K/Fe, for example, was quite different in the fine and coarse fractions from a slash burn (1.5 vs. 0.3) [33] and Pb/Br, which has been popular as an automobile exhaust tracer, varies with the "age" of urban particles [22]. 

But isotope fractionation at climatic temperatures is a function of the frequencies of the chemical bonds [16]. We quote from Herzberg [19] as follows "One would expect the -C-H bond to have essentially the same electronic structure and therefore the same force constant in different molecules, and similarly for other bonds. This is indeed observed". For the -C-H bonds the vibrational frequencies in lignin and in cellulose are almost equal, but in fact differ by 6 percent [19] because cellulose is a multiple alcohol (H-C-0-H)n and lignin is a polymer containing... 

If we had chosen to describe composition in terms of elements, we would need to carry the elemental compositions of all species, minerals, and gases, as well as the coefficients of the independent chemical reactions. Our choice of components, however, allows us to store only one array of reaction coefficients, thereby reducing memory use on the computer and simplifying the forms of the governing equations and their solution. In fact, it is possible to build a complete chemical model (excluding isotope fractionation) without acknowledging the existence of elements in the first place ... 

The strong conceptual link between stable isotopes and chemical reaction makes it possible to integrate isotope fractionation into reaction modeling, allowing us to predict not only the mineralogical and chemical consequences of a reaction process, but also the isotopic compositions of the reaction products. By tracing the distribution of isotopes in our calculations, we can better test our reaction models against observation and perhaps better understand how isotopes fractionate in nature. 

Another incremental process consists in the progressive flushing of a porous rock by a fluid. Solid-liquid exchange leads to chemical changes when more fluid is allowed to percolate, which is extremely efficient in producing strong elemental or isotopic fractionation. 

At equilibrium, the heavy isotopes of an element will tend to be concentrated in substances where that element forms the stiffest bonds (i.e., bonds with high spring constants). The magnitude of the isotopic fractionation will be roughly proportional to the difference in bond stiffness between the equilibrated substances. Bond stiffness is greatest for short, strong chemical bonds these properties correlate with ... 

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