Isotope effect on the anomalies of water: a corresponding states analysis

Light and heavy water show similar anomalies in thermodynamic and dynamic properties, with a consistent trend of anomalies occurring at higher temperature in heavy water. Viscosity also increases faster upon cooling in heavy water, causing a giant isotope effect, with a viscosity ratio near 2.4 at 244 K. While a simple temperature shift apparently helps in collapsing experimental data for both isotopes, it lacks a clear justification, changes value with the property considered, and requires additional ad hoc scaling factors. Here we use a corresponding states analysis based on the possible existence of a liquid-liquid critical point in supercooled water. This provides a coherent framework which leads to the collapse of thermodynamic data. The ratio between dynamic properties of the isotopes is strongly reduced. In particular, the decoupling between viscosity $\eta$ and self-diffusion $D$, measured as a function of temperature $T$ by the Stokes-Einstein ratio $D\eta/T$, is found to collapse after applying the corresponding states analysis. Our results are consistent with simulations and suggest that the various isotope effects mirror the one on the liquid-liquid transition.