NMR study of compressed supercritical water

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Abstract
The proton spin–lattice relaxation time T1 in water has been measured as a function of pressure in the temperature range 150 to 700°C. This study focuses on the supercritical region (tc=374°C) where the spin–rotation interaction mechanism dominates the observed proton relaxation rate. Since water is an asymmetric top molecule, the analysis of the experimental data involves a number of simplifying assumptions discussed in detail. The experimental finding that in supercritical water the spin–rotation relaxation time T 1SR is a linear function of density ρ, up to relatively high densities (ρ≃ 1.5 ρc) provides rationale for analysis of the NMR experimental data in terms of a model used for dilute gases. The T 1SR data are analyzed on the basis of the assumption that the collision modulated spin–rotation interactions can be described by a single correlation function which is an exponential function of time. Using this procedure, we find that T 1SR/ρ αT−2, i.e.T 1SR/ρ exhibits a stronger temperature dependence than that found (T 1SR/ρ αT−3/2) for many polar and nonpolar gases. The calculated effective cross sections for the transfer of angular momentum σeff which show strong temperature dependence (σeff αT−1.5) are several times larger than the kinetic cross sections. By assuming applicability of expressions derived for isotropic reorientation of spherical-top molecules and using the effective spin–rotation interaction constant as obtained from microwave measurements, we are able to calculate the angular momentum correlation time τJ, over the range of temperatures and densities studied. In the supercritical region τJ⩾τΘ, where τΘ is the reorientational correlation time, and the estimated mean angle of reorientation ΔΘ¯ is in the range 50° to 800°. The T 1SR data are also interpreted in terms of the modified rough hard sphere (RHS) model which for ρ<2ρc takes into account the effect of attractive forces. We find that 1/T 1SR is a linear function of the Enskog relaxation time τE. The experimental ratio of τE/τJ reflecting the efficiency of angular momentum transfer shows density and temperature dependence, in agreement with expectation. There is no quantitative agreement between τE/τJ calculated and observed because of the oversimplified treatment used. An empirical relationship between T 1SR and the shear viscosity in the supercritical compressed water is established, namely, the T 1SR is a linear function of the logarithm of shear viscosity. In addition, the relaxation data in the temperature range 150 to 350°C is also reported and analyzed. In this specific temperature range, both the dipolar (intra- and intermolecular) and the spin–rotation interaction mechanisms contribute to the observed proton relaxation rate.