Fractionation theory

Applying Stable Isotope Fractionation Theory to New Systems... 

Stable Isotope Fractionation Theory Applied to New Systems T1... 

APPLYING STABLE ISOTOPE FRACTIONATION THEORY Estimating unknown vibrational frequencies... 

It should be clear from the preceding discussions that practical application of equilibrium stable isotope fractionation theory often requires a certain amormt of simplification of complex and poorly studied systems. Given this reality, one should not be surprised to find that theoretically determined equilibrium fractionations rarely achieve accuracies approaching the nominal precisions of measurements made with modem analytical techniques. It should... 

BASIC KINETIC STABLE ISOTOPE FRACTIONATION THEORY... 

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... 

This chapter was improved by thoughtful suggestions from E.A. Johnson, T. Chacko, A. D. Anbar, J. R. O Neil and C. M. Johnson. 1 would also like to thank H. R Taylor, Jr. for introducing me to stable isotope fractionation theory, and G. R. Rossman for making vibrational spectroscopy fun. 

Schauble EA (2004) Applying stable isotope fractionation theory to new systems. Rev Mineral Geochem 55 65-111... 

Savin SM, Epstein S (1970b) The oxygen and hydrogen isotope geochemistry of ocean sediments and shales, Geochim Cosmochim Acta 34 43-63 Savin SM, Lee M (1988) Isotopic studies of phyUosUicates, Rev Miner 19 189-223 Schauble EA (2004) Applying stable isotope fractionation theory to new systems. Rev Miner Geochem 55 65-111... 

Three-Dimensional Effects in Field-Flow Fractionation Theory Victor P. Andreev... 

Certainly one of the major experimental difficulties of organic chemistry is the separation and isolation of individual compounds from mixtures. The term active principles has been placed in the title with the thought that if it were only called Fractionation Theory or The Art of Separating Mixtures , little interest would be aroused. Nonetheless, to the organic chemist the problem of isolating an active principle is basically no different than any other problem of fractionation with the exception that the presence of a particular compound or group of compounds has been indicated by a specific biological response. 

Although extraction is one of the oldest procedures of organic chemistry, it is usually applied in such a manner that results only approximate in nature are obtained. Purity studies require quantitative data. Particularly in biological circles, it has been appreciated for some time that if enough cases are at hand, the results can be treated statistically and thereby greater precision achieved. Therefore, multiple extractions were performed in countercurrent manner so that the steps of the binomial expansion were exactly followed (see Fractionation Theory p. 292). Tliis permitted the mathematics of probability to be applied in the... 

I. The isolatian of active principles Fractionation theory. With 7 figures. 292... 

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