A simple quantum statistical thermodynamics interpretation of an impressive phase diagram pressure shift upon (H/D) isotopic substitution in water + 3-methylpyridine

In a previous work (J. Phys. Chem. B 2003, 107, 9837), we reported liquid-liquid-phase splitting at negative pressures in mixtures of H ₂O + D₂O + 3-methylpyridine (3-MP) at the limit of pure H₂O as the solvent, thus extending for the first time the L-L phase diagrams to this metastable region. We showed that there is an intimate relation between pressure and solvent deuterium content. Isotopic substitution (H/D) in water provokes subtle entropic effects that, in turn, trigger a significant pressure shift, opening a pressure-wide miscibility window of as much as 1600 bar. Isotope effects are quantum in origin. Therefore, a model that is both pressure-dependent and considers quantization constitutes a necessary tool if one wishes to fully describe the p, T, x critical demixing in these systems. In the current work, the statistical-mechanical theory of isotope effects is combined with a compressible pressure-dependent model. This combination enabled us to predict successfully the overall L-L phase diagram via differences in the vibrational mode frequencies of water on its transfer from the pure state to that of dilution in 3-MP: each of the three librational modes undergo a calculated red-shift of -(250 ± 30) cm^-1, while the overall internal frequencies contribution is estimated as a total +(400 ± 25) cm^-1 blue-shift.