Structural relaxation in supercooled water by time-resolved spectroscopy

1. Structural relaxation in supercooled waterby time-resolved spectroscopy Renato Torre et al., Nature, 428, 296 (2004) Miyasaka Laboratory Akiko Nagafuji

2. Contents • Introduction ・Anomaly of water and supercooled water • Theory ・What is glass transition ? ・Mode-coupling theory (MCT) • Experimental ・Principle of optical Kerr effect (OKE) ・OKE experimental set-up ・What can be measured by OKE ? • Results & Discussions • Summary

3. Introduction Water Melting point & boiling point …anomalously high temperature

4. Introduction Water The density of ice …smaller than that of liquid water Masakazu Matsumoto et al., Nature, 416, 409 (2002) Because of Hydrogen Bonding

5. Introduction Supercooled Water Coefficient of thermal expansion （熱膨張率） Isothermal compressibility （等温圧縮率） Constant-pressure specific heat （定圧比熱） Extrapolated below 235K… Become infinite at a singularity temperature 225K Osamu Mishima et al., Nature, 396, 329 (1998)

6. g(t) t 0 g(t) t 0 Theory • Kinetics… What is glass transition ? g(t)：relaxation function • Thermodynamics… • g(t) decays to zero. • thermal equilibrium liquid • g(t) does not decay to zero. • quasi-stable state glass Pablo G. Debenedetti et al., Nature, 410, 259 (2001)

7. Theory What is mode-coupling theory (MCT) ? (MCT：モード結合理論) MCT adopts the nonlinear feedback mechanism. Prediction of MCT Cooling… • Ultrafast dynamics • β relaxation • Slow dynamics (α relaxation) Increase of the viscosity feedback relaxation…slow down Stretched exponential ● Glass transition (disappearance of ergodicity) ● (TS：critical temperature)

8. Experimental Optical Kerr effect(光カー効果) Polarized light Electric field of the light on off Orientation in the direction of the polarized light Liquid (isotropic) Structural relaxation

9. Experimental Probe beam polarization Probe beam polarization 45° Polarizer Pomp beam polarization

10. Experimental Set-up ・Heterodyne detection Utilization of a elliptically polarized probe beam ⇒Optical local oscillator I ： signal intensity ES：electric field of a signal El.o.： electric field of a local oscillator P : polarizer L : lens DA : differential amplifier Super-sensitivity & high accuracy Paolo Bartolini et al., J. Chem. Phy., 110, 8653 (1999)

11. Results & Discussions ◎In the short delay time… The intracage vibrational dynamics 185 cm-1 60 cm-1 ◎In the long delay time… The rearrangement of local (cage) structures • Rotational diffusion • Translational diffusion

12. Results & Discussions τlarge 254 K 314 K τ= 1 β=0.6 β≒ 0.6 The slow relaxation of water follows a stretched exponential function.

13. Results & Discussions The temperature dependence of the measured relaxation time τ… TS = 221±5 K , γ= 2.2±0.3 Agreement with the singularity temperature obtained from other experiments! TS : singularity temperature

14. Results & Discussions Two important new results obtained from this OKE experiment • The stretched exponential nature of the relaxation • The invariance of the stretching parameter (β= 0.6) with temperature 2… Water dynamics is characterized by a distribution of different time scales, suggesting the presence of a variety of relaxing structures whose distribution does not change notably with temperature.

15. Summary • The two important new results obtained from this OKE experiment are the stretched exponential nature of the relaxation and the invariance of the stretching parameter (β) with the temperature. • The structural relaxation of liquid and supercooled water follows the behavior predicted by the mode-coupling theory (MCT) . That is, structural relaxation in supercooled water can be explained using a fully dynamic model without invoking a thermodynamic one.