Magnitude of Diffusion- and Transverse Dispersion-Induced Isotope Fractionation of Organic Compounds in Aqueous Systems

Abstract

Determining whether aqueous diffusion and dispersion lead to significant isotope fractionation is important for interpreting the isotope ratios of organic contaminants in groundwater. We performed diffusion experiments with modified Stokes diaphragm cells and transverse-dispersion experiments in quasi-two-dimensional flow-through sediment tank systems to explore isotope fractionation for benzene, toluene, ethylbenzene, 2,6-dichlorobenzamide, and metolachlor at natural isotopic abundance. We observed very small to negligible diffusion- and transverse-dispersion-induced isotope enrichment factors (ε < −0.4 ‰), with changes in carbon and nitrogen isotope values within ±0.5‰ and ±1‰, respectively. Isotope effects of diffusion did not show a clear correlation with isotopologue mass with calculated power-law exponents β close to zero (0.007 < β < 0.1). In comparison to ions, noble gases, and labeled compounds, three aspects stand out. (i) If a mass dependence is derived from collision theory, then isotopologue masses of polyatomic molecules would be affected by isotopes of multiple elements resulting in very small expected effects. (ii) However, collisions do not necessarily lead to translational movement but can excite molecular vibrations or rotations minimizing the mass dependence. (iii) Solute–solvent interactions like H-bonds can further minimize the effect of collisions. Modeling scenarios showed that an inadequate model choice, or erroneous choice of β, can greatly overestimate the isotope fractionation by diffusion and, consequently, transverse dispersion. In contrast, available data for chlorinated solvent and gasoline contaminants at natural isotopic abundance suggest that in field scenarios, a potential additional uncertainty from aqueous diffusion or dispersion would add to current instrumental uncertainties on carbon or nitrogen isotope values (±1‰) with an additional ±1‰ at most.

Mass-Transfer-Limited Biodegradation at Low Concentrations—Evidence from Reactive Transport Modeling of Isotope Profiles in a Bench-Scale Aquifer

“…The mass-transfer rate r mt i of each substrate through the bacterial cell membrane from the bulk solution to the location of the enzymes is approximated via a linear-driving force model in which k tr i [s –1 ] is the first-order mass-transfer coefficient of compound i for diffusion into and out of the cell. We assumed that the mass-transfer coefficients of heavy and light isotopologues of BAM are identical due the negligible difference of their diffusion coefficients . In the presence of BAM, the intermediate product 2,6-DCBA is transformed inside the bacterial cell, such that the direction of the mass transfer of 2,6-DCBA is in the opposite direction.…”

“…Instead, the Rayleigh equation has been extended to explain cases of small isotope fractionation by introducing different additional factors: (a) variable degradation rates, (b) diffusion- or dispersion-induced isotope fractionation, , (c) an isotopic interference from mixing by dispersion or from secondary sources, , and (d) the diminishing effect of a mixing-controlled transport process, ,, or other physical and chemical heterogeneity. , Regarding variable degradation rates, Wanner and Hunkeler observed decreased changes in carbon isotope ratios with depth in contaminated clay, which were explained by a nonuniform, depth-dependent degradation rate due to nutrient availability in the aquitard . Our results suggest that mass-transfer limitation by cell–wall permeation could provide an alternative explanation. As per dispersion, several studies have assumed that isotopologue-specific transverse dispersion may explain isotope patterns observed in transverse profiles of steady-state plumes. , In contrast, recent work from our lab demonstrates that diffusion- and transverse dispersion-induced isotope fractionation of BAM at natural isotopic abundance in a 2-D flow-through sediment system is negligible: Diffusion- and transverse dispersion-induced isotope enrichment factors ε were smaller than −0.4‰, and changes in carbon and nitrogen isotope values were within ±0.5 and ±1‰, respectively. Thus, isotope effects of the dispersion can be excluded as an explanation of the observed isotope patterns in the present study. With regard to mixing with a secondary source, Prommer et al observed muted carbon isotope fractionation of toluene with decreasing toluene concentration at a tar oil-contaminated field site.…”

“…As per dispersion, several studies have assumed that isotopologue-specific transverse dispersion may explain isotope patterns observed in transverse profiles of steady-state plumes. , In contrast, recent work from our lab demonstrates that diffusion- and transverse dispersion-induced isotope fractionation of BAM at natural isotopic abundance in a 2-D flow-through sediment system is negligible: Diffusion- and transverse dispersion-induced isotope enrichment factors ε were smaller than −0.4‰, and changes in carbon and nitrogen isotope values were within ±0.5 and ±1‰, respectively. Thus, isotope effects of the dispersion can be excluded as an explanation of the observed isotope patterns in the present study.…”

Isotope Effects on the Vaporization of Organic Compounds from an Aqueous Solution–Insight from Experiment and Computations

“…In contrast, when an initial (liquid) state becomes enriched in lighter isotopologues, meaning that heavier moieties are more prone to evaporation, then we call such an effect inverse. Previous studies have substantiated the general rule that an observable kinetic isotope fractionation of a liquid phase-air transfer will reflect the bottleneck of the overall process. ,− If diffusion through the liquid phase is rate-limiting, the observable isotope effect that reflects a liquid phase diffusion will typically be very small. , If, however, diffusion through a stagnant air layer above the water surface is rate-limiting, the overall isotope effect may be non-negligible, and it will be a composite of the equilibrium air/solvent isotope effect and the kinetic isotope effect of diffusion through air. While isotope effects of diffusion in the gas phase can be estimated based on isotopologue masses (see, e.g., Bouchard 2011), the equilibrium isotope effect of solvent-air partitioning is less straightforward to predict.…”

“… 10 , 15 − 21 If diffusion through the liquid phase is rate-limiting, the observable isotope effect that reflects a liquid phase diffusion will typically be very small. 19 , 22 If, however, diffusion through a stagnant air layer above the water surface is rate-limiting, the overall isotope effect may be non-negligible, and it will be a composite of the equilibrium air/solvent isotope effect and the kinetic isotope effect of diffusion through air. While isotope effects of diffusion in the gas phase can be estimated based on isotopologue masses (see, e.g., Bouchard 2011 16 ), the equilibrium isotope effect of solvent-air partitioning is less straightforward to predict.…”