Calculation of vapor pressure isotope effects in the rare gases and their mixtures using an integral equation theory

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.

Isotopic Dependence of Vapor Pressure in Xenon

The vapor pressure isotopic effect (VPIE) of xenon has been measured using cryogenic distillation. The still is calibrated with argon and krypton and yields a measurement of ln(p ₁₃₀/p ₁₃₆) ≃ (0.26 ± 0.04) × 10^-3, where p ₁₃₀ and p ₁₃₆ are the vapor pressures of ¹³⁰Xe and ¹³⁶Xe at the nominal boiling point, respectively. The dependence of the VPIE across the isotopes for the three elements is found to be approximately linear with atomic mass, and all values are consistent with theoretical expectations.

Liquid-vapor equilibrium isotopic fractionation of water: how well can classical water models predict it?

The liquid-vapor equilibrium isotopic fractionation of water is determined by molecular-based simulation, via Gibbs ensemble Monte Carlo and isothermal-isochoric molecular dynamics involving two radically different but realistic models, the extended simple point charge, and the Gaussian charge polarizable models. The predicted temperature dependence of the liquid-vapor equilibrium isotopic fractionation factors for H(2) (18)O/H(2) (16)O, H(2) (17)O/H(2) (16)O, and (2)H(1)H(16)O/(1)H(2) (16)O are compared against the most accurate experimental datasets to assess the ability of these intermolecular potential models to describe quantum effects according to the Kirkwood-Wigner free energy perturbation variant Planck's over h(2)-expansion. Predictions of the vapor pressure isotopic effect for the H(2) (18)O/H(2) (16)O and H(2) (17)O/H(2) (16)O pairs are also presented in comparison with experimental data and two recently proposed thermodynamic modeling approaches. Finally, the simulation results are used to discuss some approximations behind the microscopic interpretation of isotopic fractionation based on the underlying rototranslational coupling.

Novel Corresponding-States Principle Approach for the Equation of State of Isotopologues: H218O as an Example

The corresponding-states principle (CSP) has been considered for the development of the equations of state (EOS) of minor isotopologues that are usually unknown. We demonstrate that, for isotopologues of a given molecular fluid, a general extended multi-parameter corresponding-states EOS can be reduced to the three-parameter EOS, utilizing the critical parameters (temperature and density) and Pitzer's acentric factor as correlation parameters. Appropriate general CSP mathematical formalism and equations for constructing the EOS of minor isotopologues are described in detail. The formalism and equations were applied to isotopologues of water and demonstrated that the isotopic effect on the critical parameters and the acentric factor of H(2)(18)O can be successfully calculated from the EOS of H2O and experimental data on the isotope effects (liquid-vapor isotope fractionation factor and molar volume isotope effect). We have also shown that the experimental data on the vapor pressure isotope effect (VPIE) for 18O-substituted water are inconsistent within the framework of thermodynamics with the liquid-vapor oxygen isotope fractionation factor. The novel approach of CSP to isotopologues developed in this study creates a new opportunity for constructing the EOS of minor isotopologues for many other molecular fluids.

Liquid-vapor isotopic fractionation factors of diatomic fluids: A direct comparison between molecular simulation and experiment

Liquid-vapor fractionation factors of molecular fluids are studied by molecular-based simulation, Gibbs ensemble Monte Carlo, and isothermal-isochoric molecular dynamics of realistic models for N(2), O(2), and CO. The temperature dependence of the fractionation factors for (15)N(14)N(14)N(2), (15)N(2)(14)N(2), (18)O(16)O(16)O(2), (18)O(2)(16)O(2), (13)C(16)O(12)C(16)O, and (12)C(18)O(12)C(16)O along the vapor-liquid coexistence curves as predicted by simulation is compared with the existing experimental data to assess the accuracy of Planck's(2)-order Kirkwood-Wigner free energy expansion for specific model parametrizations. Predictions of the fractionation factors for other isotopologue pairs, including (18)O(17)O(16)O(2), (16)O(17)O(16)O(2), and (17)O(2)(16)O(2), as well as tests of some approximations behind the microscopic interpretation of the fractionation factors are also given.