Temperature Dependence of Isotopic Quantum Effects in Water

The technique of high energy x-ray diffraction has been used to measure the temperature variation of hydrogen versus deuterium isotopic quantum effects on the structure of water. The magnitude of the effect is found to be inversely proportional to the temperature, varying by a factor of 2.5 over the range 6 to 45 °C. In addition, the ${\mathrm{H}}_2{}^{16}\mathrm{O}$ versus ${\mathrm{H}}_2{}^{18}\mathrm{O}$ effect has been measured at 26 °C and the structural difference shown to be restricted to the nearest neighbor molecular interactions. The results are compared to recent simulations and previously measured isochoric temperature differentials; additionally, implications for $\mathrm{H}/\mathrm{D}$ substitution experiments are considered.

Figure 1

Difference electronic structure factor, $\Delta S_X(Q)$, for light minus heavy water measured at SPring-8. Top: ${\mathrm{H}}_2\mathrm{O}\mathrm{\text{−}}{\mathrm{D}}_2\mathrm{O}$ at 26.2 °C (shifted by $+1.4$). Bottom: ${\mathrm{H}}_2{}^{16}\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}_2{}^{18}\mathrm{O}$ at 26.4 °C. Error bars for either data set are shown as vertical lines through the data points.

Figure 2

Isotope quantum effect as a function of temperature measured at HASYLAB. (a) $\Delta S_X(Q)$ for ${\mathrm{H}}_2\mathrm{O}\mathrm{\text{−}}{\mathrm{D}}_2\mathrm{O}$ at (from top to bottom) 45, 35, 23, 15, and 6 °C with error bars. (b) Summations over $\Delta S_X(Q)$ for ${\mathrm{H}}_2\mathrm{O}\mathrm{\text{−}}{\mathrm{D}}_2\mathrm{O}$ (squares, HASYLAB; triangle, SPring-8) and ${\mathrm{H}}_2{}^{16}\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}_2{}^{18}\mathrm{O}$ [circle; see Eq. (2) for description of summation].

Figure 3

Solid lines: Difference correlation functions, $\Delta g(r)$, for ${\mathrm{H}}_2\mathrm{O}\mathrm{\text{−}}{\mathrm{D}}_2\mathrm{O}$ at (from top to bottom) 45, 35, 23, 15, and 6 °C. Dashed lines: Isochoric temperature differentials (ITD) from Bosio et al. [14] scaled by $\Delta T$ (from top to bottom): 3.6, 4.3, 5.1, 5.6, and 7.1 °C.

Figure 4

(a) ${\mathrm{H}}_2{}^{16}\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}_2{}^{18}\mathrm{O}$ difference correlation function (solid line) compared to quantized minus classical path-integral MD simulation from Kuharski and Rossky (dashed line) [3]. (b) A comparison of ${\mathrm{H}}_2\mathrm{O}\mathrm{\text{−}}{\mathrm{D}}_2\mathrm{O}$ difference data at 35 °C (upper solid line) with simulation results from Chen et al. [7] (dashed line) and experimental 6 °C data (lower solid line) with Guillot and Guissani [5] (dot-dashed line). Details are given in Ref. 18.