The temperature dependences of the vapor pressure of light (p_l) and heavy (p_h) isotopologues are known to be different, even though, their differences are of the order of thousandths, i.e., , and consequently, the study of isotopic vapor pressure effect requires extremely precise measurements. From a chemical thermodynamics viewpoint, these isotopic effects correspond to extremely small changes of free energies of quantum nature, their modeling becomes also rather troublesome and therefore, requiring special approaches.

Isotopic vapor pressure effects have been the focus of much attention since the first theoretical studies by Lindemann (Lindemann, 1919) and Urey et al. (Urey et al., 1932) who predicted larger volatility of the lighter isotope for simple substances. While this prediction applies strictly to atomic isotopologues for which the isotopic effect can be associated with their translational degrees of freedom, it breaks down for molecular isotopologues, where the effect originates not only from translational but also rotational degrees of freedom, and their potential roto-translational couplings.

While the isotopic effect on the vapor pressure is usually measured (Calado et al., 2000) as the ratio of vapor pressure of the pure isotopes, , the liquid-vapor isotope fractionation factor () (where and denote the mole fraction of the isotope in the condensed and the vapor phase, respectively, and and indicate light and heavy isotopes) rather than (Bigeleisen and Roth, 1961) offers better insight into the molecular driving forces underlying the isotopic effects on the behavior of the isotopologues.

We have recently reported on the prediction of the for noble gases based on the Kirkwood-Wigner (KW) truncated perturbation expansion of the Helmholtz free energy around the classical limit (Chialvo and Horita, 2003). In particular, we highlighted the remarkable agreement between simulation predictions and the most accurate experimental data available for the vapor-liquid and vapor-solid fractionation of argon isotopes, which provided strong support to the adequacy of the truncated KW expansion. We have also illustrated that the KW expansion for the isotope fractionation factor does not converge at the terms for neon, i.e., requiring the inclusion of the terms to bring the simulation predictions to an excellent agreement with the experimental data. Furthermore, we performed successfully, and for the first time ever, the simulation prediction of for mixtures of noble gases, and compared with the only set of experimental data available.

In this work we report the prediction of for molecular fluids based on the truncated KW expansion of the quantum Helmholtz free energy expression for rigid polyatomic fluids. In particular, we focus on (a) the adequacy of off-the-shelf parameterizations to predict in polyatomic gases; (b) the analysis of the roto-translational coupling effect in asymmetric isotopic substitution involving homo- and hetero-nuclear molecules, (c) the prediction of isotope fractionation factors for systems, and/or conditions not currently available, and (e) the accuracy of some approximations used in the modeling and interpretation of isotope fractionation.

Toward that end, we have determined the liquid-vapor fractionation factors of molecular fluids by molecular-based simulation, via Gibbs Ensemble Monte Carlo and isothermal-isochoric molecular dynamics of realistic models for , , and . In particular, we study the temperature dependence of the fractionation factors for , , , , , and along the vapor-liquid coexistence curves as predicted by simulation and compared with the existing experimental data, to assess the accuracy of order Kirkwood-Wigner free energy expansion for specific model parameterizations. Finally, we invoked some underlying roto-translational correlations to propose and test a couple of novel expressions to predict of homo-nuclear diatomics based solely on the experimental values of either the mean squared forces or the mean squared torques obtained from spectroscopic measurements.

REFERENCES:

Bigeleisen J. and Roth E. (1961) Vapor Pressure of the Neon Isotopes. Journal of Chemical Physics 35, 68-77.

Calado J. C. G., Dias F. A., Lopes J. N. C., and Rebelo L. P. N. (2000) Vapor Pressure and Related Thermodynamic Properties of ³⁶Ar. Journal of Physical Chemistry B 104, 8735-8742.

Chialvo A. A. and Horita J. (2003) Isotopic Effect on Phase Equilibria of Atomic Fluids and their Mixtures: A Direct Comparison between Molecular Simulation and Experiment. Journal of Chemical Physics 119(8), 4458-4467.

Lindemann F. A. (1919) Note on the Vapor Pressure and Affinity of Isotopes. Philosophycal Magazine 38, 173-181.

Urey H. C., Brickwedde F. G., and Murphy G. M. (1932) A Hydrogen Isotope of Mass 2 and its Concentration. Physical Review 40, 1-.

This research was sponsored by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences under contract number DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.