Temperature dependency of the triple isotope fractionation relationship for equilibrium processes

Abstract:

The use of an approximation to the Bigeleisen-Mayer-Urey model for isotope fractionation has led to the concept of a constant, and later constrained, mass fractionation law for multiple isotopes of the same element. This concept has brought new insights to investigation in photochemistry, radical chemistry, or the contribution of quantum tunneling to chemical and biological processes. Despite previous work indicating that these mass fractionation laws can be highly variable, the concept of a constant relationship remains common in these fields. Using the diatomic case as a first-order approximation, we demonstrate generically that the mass fractionation exponent, θ, can take any value for small fractionations but is less variable for large fractionations. The predicted variability is larger than both theoretical and analytical precision. These deviations from the traditional range of mass-dependence exponents are the largest under cross-over scenarios, but can occur for any scenario with small fractionations. We advocate the use of ∆∆^‡M or “change in cap-delta”, defined strictly with a slope of at the high-temperature limit, as a necessary, more reliable and more useful descriptor of mass-dependent fractionation. This work can bring new insights and a conventional explanation to low temperature experiments yielding traditionally unusual mass fractionation laws.