Solubility Equilibrium Isotope Effects of Noble Gases in Water: Theory and Observations

The abundance and isotopic composition of noble gases dissolved in water have many applications in the geosciences. In recent years, new analytical techniques have opened the door to the use of high-precision measurements of noble gas isotopes as tracers for groundwater hydrology, oceanography, mantle geochemistry, and paleoclimatology. These analytical advances have brought about new measurements of solubility equilibrium isotope effects (SEIEs) in water (i.e., the relative solubilities of noble gas isotopes) and their sensitivities to the temperature and salinity. Here, we carry out a suite of classical molecular dynamics (MD) simulations and employ the theoretical method of quantum correction to estimate SEIEs for comparison with experimental observations. We find that classical MD simulations can accurately predict SEIEs for the isotopes of Ar, Kr, and Xe to order 0.01‰, on the scale of analytical uncertainty. However, MD simulations consistently overpredict the SEIEs of Ne and He by up to 40% of observed values. We carry out sensitivity tests at different temperatures, salinities, and pressures and employ different sets of interatomic potential parameters and water models. For all noble gas isotopes, the TIP4P water model is found to reproduce observed SEIEs more accurately than the SPC/E and TIP4P/ice models. Classical MD simulations also accurately capture the sign and approximate magnitude of temperature and salinity sensitivities of SEIEs for heavy noble gases. We find that experimental and modeled SEIEs generally follow an inverse-square mass dependence, which implies that the mean-square force experienced by a noble gas atom within a solvation shell is similar for all noble gases. This inverse-square mass proportionality is nearly exact for Ar, Kr, and Xe isotopes, but He and Ne exhibit a slightly weaker mass dependence. We hypothesize that the apparent dichotomy between He-Ne and Ar-Kr-Xe SEIEs may result from atomic size differences, whereby the smaller noble gases are more likely to spontaneously fit within cavities of water without breaking water-water H-bonds, thereby experiencing softer collisions during translation within a solvation shell. We further speculate that the overprediction of simulated He and Ne SEIEs may result from the neglection of higher-order quantum corrections or the overly stiff representation of van der Waals repulsion by the widely used Lennard-Jones 6-12 potential model. We suggest that new measurements of SEIEs of heavy and light noble gases may represent a novel set of constraints with which to refine hydrophobic solvation theories and optimize the set of interatomic potential models used in MD simulations of water and noble gases.