Experimental Determination of the Structural Relaxation in Liquid Water

The investigation of large wavevector excitations in liquid water has shown the existence of a positive dispersion in the velocity of sound. This dispersion has been inferred in the pioneering computational [1] and experimental [2] studies of the dynamic structure factor, S(Q,E), and has been recently assessed by Inelastic X-ray Scattering (IXS) [3]. Using IXS, the transition of the longitudinal sound velocity from the adiabatic value, c_o ~ 1500 m/s, to a value more than twice larger, c ~ 3200 m/s, was studied at T = 5°C. This sound velocity dispersion is qualitatively similar to that observed in glass-forming liquids. There, the transition between the two dynamic regimes is determined by the coupling of the propagating density fluctuations with the dynamics of the structural rearrangements of the particles in the liquid. The complex dynamics of such a rearrangement can be described by a relaxation process with a characteristic time, . The transition takes place when the condition ~ 1 is fulfilled. In glass-forming liquids has a very steep temperature dependence; its typical values are in the nanosecond range close to the melting point and dramatically increases near the calorimetric glass transition temperature T_g. This relaxation process (-process) has a cooperative nature and the density fluctuations are influenced differently in the two opposite frequency limits: the system has a solid like elastic behaviour for >> 1, and a viscous one for << 1. One could speculate that also in liquid water the physical mechanism responsible for the dispersion of the sound velocity is an -relaxation process.

The experimental characterisation of the -process is typically obtained by the determination of the dispersion of the sound velocity as a function of T and at a constant Q transfer value. At the inflection point "t" of such an "S"-shaped curve the condition _t(Q,T)(T) ~ 1, with (Q,T) = c_app(Q,T) Q, is fulfilled. In glass forming liquids, this condition is met by Brillouin Light Scattering (BLS) measurements close to melting, and by Ultrasonic (US) methods close to T_g. Indeed, the typical frequencies allowed by these two techniques are such that (Q,T)(T) ~ 1 is met for values of in the 100 ps (BLS) and 1 µs (US) ranges. In the case of water, as a consequence of the small value of close to melting, the BLS cannot access the relevant excitations energy region. The complete determination of the "S"-shaped curve as a function of either T or Q requires, however, the use of IXS [3].

This scenario has motivated an experiment on the ultra­high energy resolution inelastic X-ray scattering spectrometer of ID16 on the temperature dependence of the transition from normal to fast sound in liquid water in the T = 260-570 K and Q = 1-12 nm^-1 regions. In order to emphasise the thermal effects, and to minimise the modification of the hydrogen bond dynamics due to large variations of the excluded volume, the density was kept in the range = 0.94-1.07 g/cm³. This was obtained adjusting the pressure in the 0-2 kbar range. The existence of a relaxation process is demonstrated by Figure 52 which shows that the transition between the two sound regimes takes place at increasing Q values with increasing temperatures. The associated time-scale extends into the sub-picosecond region with increasing temperature.

The analogy with the glass-formers phenomenology, implies that the fast relaxation process studied in this work can be identified with an -process. The derived values of are consistent with previous estimations: they roughly follow an Arrhenius behaviour with an activation energy comparable to the hydrogen bond energy. This suggests that, in water, the -process is associated with the rearrangement (making and breaking) of molecular structures kept together by the hydrogen bond.

The IXS data were analysed both with an empirical model and with a visco-elastic model, and in each case it was possible to determine the detailed T and Q dependence of the relaxation time, .

References
[1] Rahman and Stillinger, Phys. Rev., A 10, 368 (1974).
[2] J. Teixeira, M.C. Bellisent-Funel, S.H. Chen, B. Doznez, Phys. Rev. Lett., 54, 2681 (1985).
[3] F. Sette et al., Phys. Rev. Lett., 75, 850 (1995); Phys. Rev. Lett., L77, 83 (1996).

Principal Publications and Authors
A. Cunsolo (a), G. Ruocco (b), F. Sette (a), C. Masciovecchio (a), A. Mermet (a), G. Monaco (b), M. Sampoli (a), R. Verbeni (a), Phys. Rev. Lett., 82, 775 (1999).
G. Monaco, A. Cunsolo, G. Ruocco, F. Sette, Phys. Rev., E 60, 5505 (1999).

(a) ESRF
(b) Università di L'Aquila and Istituto Nazionale di Fisica della Materia (Italy)
(c) Università di Firenze and Istituto Nazionale di Fisica della Materia (Italy)