Pressure effects on the reduced partition function ratio for hydrogen isotopes in water

We have developed a simple, yet accurate theoretical method for calculating the reduced isotope partition function ratio (RIPFR) for hydrogen of water at elevated pressures. This approach requires only accurate equations of state (EOS) for pure isotopic end-members (H₂O and D₂O), which are available in the literature. The effect of pressure or density on the RIPFR of water was calculated relative to that of ideal-gas water at infinitely low pressure for the temperature range from 0 to 527 °C. For gaseous and low-pressure (ca. {less-than or slanted equal to}15 MPa) supercritical phases of water, the RIPFR increases slightly (1-1.3‰) with pressure or density in a fashion similar to those of many other geologic materials. However, in liquid and high-pressure (>20 MPa) supercritical phases, the RIPFR of water decreases (0.5-6‰) with increasing pressure (or density) to 100 MPa. This rather unique phenomenon is ascribed to the inverse molar volume isotope effects (MVIE) of liquid and high-density supercritical waters, V (D₂O) > V (H₂O), while other substances including minerals show the normal MVIE. These theoretical predictions were experimentally confirmed by Horita et al. [Horita, J., Cole, D.R., Polyakov, V.B., Driesner, T., 2002. Experimental and theoretical study of pressure effects on hydrogen isotope fractionation in the system brucite-water at elevated temperatures. Geochim. Cosmochim. Acta 66, 3769 - 3788.] for the system brucite-water. Although the P-T ranges for the EOS of normal and heavy waters are rather limited, our modeling indicates that the RIPFR of water continues to decrease with pressure above 100 MPa. The method developed here can be applied to any other geologic fluids, if accurate EOS for their isotopic end-members is available. These results have important implications for the interpretation of high-pressure isotopic partitioning in the Earth, the outer planets, and their moons.