Pressure- and temperature-variable viscosity dependencies of rotational correlation times for solitary water molecules in organic solvents

Deuteron nuclear magnetic resonance spin-lattice relaxation times T1 have been measured for solitary water molecules (D2O) at low concentrations in apolar and polar organic solvents at 30 °C at high pressures; D2O (30 mM) in C6H6 up to 90 MPa, D2O (60 mM) in CHCl3 up to 300 MPa, D2O (100 mM) in CH3CN up to 300 MPa. The rotational correlation times τ2R for D2O in the organic solvents increase with increasing pressure. The pressure effect on τ2R for D2O in solution is considerably larger than that on τ2R and η (viscosity) for the neat solvent. We have tested the two forms of modified Stokes–Einstein–Debye law; the linear and nonlinear forms are τ2R=τ02R+S(η/T) and τ2R=B(η/T)α, respectively. The rotational correlation times are linearly related to solvent viscosity divided by temperature (η/T) with a large positive intercept (τ02R≳0). It is shown that the linear form is practically better, and that the nonlinear form constrained at η/T=0 is invalid. The temperature-variable slope (ST) and the pressure-variable one (Sp) are markedly different, the ratios of Sp to ST being 0.2–0.3. The extended-diffusion models based on isolated binary collisions cannot be used to explain the observed pressure effect because of the neglect of the attractive solute–solvent interactions.