Breakdown of the Stokes-Einstein relation in supercooled water.

A lmost everyone would agree that water is probably the most important liquid for life, but few fully appreciate that water is also the most puzzling among the liquids. Water is anomalous in many ways compared with simple liquids. One of the most well known anomalies is the decrease of density of water upon cooling below 4°C. Other anomalies of water include the increase of specific heat and compressibility upon cooling. Apart from the thermodynamic anomalies, the dynamics of water also displays surprising properties, such as the increase of diffusivity and decrease of viscosity upon compression (1) and a breakdown of the Stokes–Einstein (SE) relation (2) in supercooled water. The SE relation is a hydrodynamic equation relating the diffusivity, D, the temperature, T, and relaxation time, ! (assuming that ! is proportional to the viscosity). Specifically, it states that D is proportional to T and inversely proportional to the relaxation time !. Hence, the product D!!T should be temperature independent. This important hydrodynamic relation is obeyed by many liquids (3, 4) at relatively high temperatures, but it usually fails to describe the dynamics in supercooled states. Breakdown of the SE relation has also been seen in simple liquids near the glass transition (3–6). It was hypothesized that the presence of large dynamic heterogeneities might cause the breakdown of SE relation (7, 8). Dynamic heterogeneities in liquids are the consequence of highly mobile molecules forming a cluster and moving cooperatively. The size of these spatially heterogeneous dynamical regions increases as the temperature is decreased. Dynamic heterogeneities facilitate diffusion (and local strucutral relaxation) but do not facilitate the relaxation of the entire system. Hence, the large size of these dynamic heterogeneities should ‘‘decouple’’ diffusion and relaxation so D!!T is no longer a constant. The presence of dynamic heterogeneities in supercooled liquids has been verified by both experiments (6, 9) and computer simulations (10). In molecular liquids as well as in colloidal suspensions, the glass transition is followed by a sharp growth in dynamic heterogeneities (6, 9). Hence, it is common to assume that SE breakdown is related to glass transition because the sizes of dynamic heterogeneities grows sharply near the glass transition (3, 4, 8, 11, 12). In this issue of PNAS, the work by Chen et al. (13) on water confined in nanopores sheds light on the long standing issue of decoupling of diffusion and structural relaxation in supercooled water. They measure the diffusivity D by NMR experiments and the relaxation time ! by neutron scattering experiments for temperatures down to !83°C or 190 K. Confinement prevents the freezing of water below the bulk homogeneous nucleation temperature of !38°C. Chen et al. find that the product D!!T is a constant at higher temperatures but increases sharply at low temperatures, signaling the breakdown of the SE relation. They further find that the breakdown of the SE relation occurs well above water’s glass transition temperature (13). Hence, their experiments call out for a scenario different from that believed for simple colloidal suspensions and liquids. A possible clue for this new scenario arises from the fact that Chen et al. discover that the SE relation breaks down at the same temperature where the behavior of the dynamics of water changes from non-Arrhenius at high temperatures to Arrhenius at low temperatures, which is estimated to be "136 K (14). One possible interpretation of the breakdown of SE relation in supercooled water consistent with experimental results (15) is the presence of a hypothesized liquid–liquid critical point (16, 17) in the deep supercooled region of water. The liquid–liquid critical point gives rise to a Widom line TW(P) (see Fig. 1), the locus of the correlation length maxima, which emanates from the liquid–liquid critical point and extends into the one-phase region