Scaled Polynomial Expression for Self-Diffusion Coefficients for Water, Benzene, and Cyclohexane over a Wide Range of Temperatures and Densities

Abstract

Self-diffusion coefficients D for water, benzene, and cyclohexane were determined in high-temperature conditions along the liquid branch of the coexistence curve and in supercritical conditions including an extremely low density region. The diffusion data available in literature were compared and evaluated. A fifth-order polynomial for ln D with the single variable T −1 (ln(D/10−9 m2·s−1) = a 0+ a 1 x + a 2 x 2 + a 3 x 3 + a 4 x 4 + a 5 x 5 with x = 1000/(T/K)) was found to provide good fitting along the liquid branch of the coexistence curve. A single polynomial function for the scaled quantity ρD/T 1/2 with the two variables, density ρ and temperature T −1 (third-order polynomial of ρ and T −1 and the cross terms), can universally represent the diffusion data over a wider range including both the gas−liquid coexistence and the extremely low density conditions. The function gives a reliable and reasonable behavior of D in the medium-density supercritical states in which the experimental uncertainty is rather large due to the severe conditions. The temperature and density differentials thus obtained were used to shed light on the effect of hydrogen bonding that makes water different from nonpolar organic liquids. The temperature dependence of the self-diffusion coefficient for water is larger than those for organic liquids, due to the large contribution of the attractive hydrogen-bonding interaction. The density dependence is larger for organic liquids than that for water.

Tests of the Stokes–Einstein Relation through the Shear Viscosity Activation Energy of Water

“…The present simulations give D = 2.382 × 10 –5 cm 2 /s after applying this correction. This is in good agreement with the accepted best value from measurements of 2.229 × 10 –5 cm 2 /s. ,− Interestingly, within the Stokes–Einstein approximation (see the Appendix), the correction for finite-size effects in eq yields the same activation energy for D and D PBC , so no adjustment is required for E a, D . If the Stokes–Einstein relation is not assumed, eq can be used to obtain the “corrected” activation energy for D and gives E a, D = 4.40 ± 0.08 kcal/mol, which is only 0.13 ± 0.08 kcal/mol larger than E a, D PBC , indicating that these corrections are small.…”

Supercritical water anomalies in the vicinity of the Widom line

“…Yoshida et al . 53 use a function based on the scaling to the hard-sphere model. The Widom points are described by filled symbols.…”

Tetrapropylammonium Occlusion in Nanoaggregates of Precursor of Silicalite-1 Zeolite Studied by 1H and 13C NMR

“…2400, 1300 and 750 µm 2¨s´1 , respectively, at extreme dilution. The limiting values extrapolated to pure water are 2300, 1230, and 820 µm 2¨s´1 respectively for water [67,68], ethanol [69] and TPA [70]. DLS measurements on the same system exhibited for nanoparticles diffusion coefficients D varying between 16 and 96 µm 2¨s´1 when x was varied from 152 to 8000 [62].…”