Sulfur isotope biogeochemistry

Sulfur isotope biogeochemistry is the study of the distribution of sulfur isotopes in biological and geological materials. In addition to its common isotope, 32S, sulfur has three rare stable isotopes: 34S, 36S, and 33S. The distribution of these isotopes in the environment is controlled by many biochemical and physical processes, including biological metabolisms, mineral formation processes, and atmospheric chemistry. Measuring the abundance of sulfur stable isotopes in natural materials, like bacterial cultures, minerals, or seawater, can reveal information about these processes both in the modern environment and over Earth history.

Background

Natural abundance of sulfur isotopes

Sulfur has 24 known isotopes, 4 of which are stable (meaning that they do not undergo radioactive decay). 32S, the common isotope of sulfur, makes up 95.0% of the natural sulfur on Earth. In the atomic symbol of 32S, the number 32 refers to the mass of each sulfur atom in daltons, the result of the 16 protons and 16 neutrons of 1 dalton each that make up the sulfur nucleus. The three rare stable isotopes of sulfur are 34S (4.2% of natural sulfur), 33S (0.75%), and 36S (0.015%). These isotopes differ from 32S in the number of neutrons in each atom, but not the number of protons or electrons; as a result, each isotope has a slightly different mass, but has nearly identical chemical properties.

Physical chemistry Small differences in mass between stable isotopes of the same element can lead to a phenomenon called an "isotope effect," where heavier or lighter isotopes are preferentially incorporated into different natural materials depending on the materials' chemical composition or physical state. Isotope effects are divided into two main groups: kinetic isotope effects and equilibrium isotope effects. A kinetic isotope effect occurs when a reaction is irreversible, meaning that the reaction only proceeds in the direction from reactants to products. Kinetic isotope effects cause isotopic fractionation—meaning that they affect the isotopic composition of reactant and product compounds—because the mass differences between stable isotopes can affect the rate of chemical reactions. It takes more energy to reach the transition state of a reaction if the compound has bonds with a heavier isotope, which causes the compound with heavier isotopes to react more slowly. Normal kinetic isotope effects cause the lighter isotope (or isotopes) to be preferentially included in a reaction's product. The products are then said to be "depleted" in the heavy isotope relative to the reactant. Rarely, inverse kinetic isotope effects may occur, where the heavier isotope is preferentially included in a reaction's product. Equilibrium isotope effects cause fractionation because it is more chemically favorable for heavy isotopes to take part in stronger bonds. An equilibrium isotope effect occurs when a reaction is at equilibrium, meaning that the reaction is able to occur in both directions simultaneously. When a reaction is at equilibrium, heavy isotopes will preferentially accumulate where they can form the strongest bonds. For example, when the water in a sealed, half-full bottle is in equilibrium with the vapor above it, the heavier isotopes 2H and 18O will accumulate in the liquid, where they form stronger bonds, while the lighter isotopes 1H and 16O will accumulate in the vapor. The liquid is then said to be "enriched" in the heavy isotope relative to the vapor.

Calculations

Delta notation Differences in the abundance of stable isotopes among natural materials are usually very small (natural differences in the ratio of rare to common isotope are almost always below 0.1%, and sometimes much smaller). Nevertheless, these very small differences can record meaningful biological and geological processes. To facilitate comparison of these small but meaningful differences, isotope abundances in natural materials are often reported relative to isotope abundances in designated standards. The convention for reporting the measured difference between a sample and a standard is called "delta notation." For example, imagine an element X for which we wish to compare the rare, heavy stable isotope with atomic mass A (AX) to the light, common isotope with atomic mass B (BX). The abundance of AX and BX in any given material is reported with the notation δAX. δAX for the sample material is calculated as follows:

AR = (total amount of AX)/(total amount of BX) δAXsample = (ARsample − ARstandard)/ARstandard δ values are most commonly reported in parts per thousand, commonly referred to in isotope chemistry as per mille and represented by the symbol ‰. To report δ values in per mille, the δ value as calculated above should be multiplied by 1000:

δAXsample (‰) = ((ARsample − ARstandard)/ARstandard) * 1000

Fractionation factors While an isotope effect is the physical tendency for stable isotopes to distribute in a particular way, the isotopic fractionation is the measurable result of this tendency. The isotopic fractionation of a natural process can be calculated from measured isotope abundances. The calculated value is called a "fractionation factor," and allows the effect of different processes on isotope distributions to be mathematically compared. For example, imagine a chemical reaction Reactant → Product. Reactant and Product are materials that both contain the element X, and X has two stable isotopes, AX (the heavy isotope, with a mass of A) and BX (the light isotope, with a mass of B). The fractionation factor for the element X in the reaction Reactant → Product is represented by the notation

AαProduct/Reactant. AαProduct/Reactant is calculated as follows: AαProduct/Reactant = (δAXProduct + 1)/(δAXReactant + 1) Fractionation factors can also be reported using the notation AεProduct/Reactant, which is sometimes called the "enrichment factor" and is calculated as follows:

AεProduct/Reactant = AαProduct/Reactant − 1 Like δ values, ε values can be reported in per mille by multiplying by 1000.

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