Decoupling of Translational Diffusion from the Viscosity of Supercooled Water: Role of Translational Jump Diffusion

Abstract

Some experiments have witnessed increasing decoupling of viscosity from the translational self-diffusion of supercooled water with decreasing temperature. While theory and computer simulation studies indicated the jump translation of the molecules as a probable origin of the above decoupling, a precise quantitative estimation is still lacking. Through a molecular dynamics (MD) simulation study, along with careful consideration of translational jump motion, we have found the most definite proof of increasing relevance of translational jump diffusion in the above decoupling phenomena. By separating out the jump-only diffusion contribution from the overall diffusion of the water, we obtain the residual diffusion coefficient, which remains strongly coupled with the viscosity of the medium at the whole temperature range, including supercooled regime. These new findings can help to elucidate many experimental studies featuring molecular transport properties, where strong diffusion-viscosity decoupling comes into the picture. 3There are intriguing properties of supercooled water, including a strong decoupling between its viscosity and the diffusion of the molecules. Some experimental studies [1][2][3] -including that by Dehaoui et al.[4]-has revealed an increasing decoupling of viscosity from the water translational diffusion coefficient upon cooling. This indicates a gradual breakdown of the Stokes-Einstein (SE) relation ( with decreasing temperature. In contrast, the rotational diffusion D r remains coupled with for a wide range of temperature, which implies the validity of the Stokes-Einstein-Debye (SED) relation. Similar decoupling between D t and  was alsoreported earlier in other molecular glass forming liquids.[5-13] The SE relation is obeyed at sufficiently high temperature, but severely breaks down around 1.3T g (T g is the glass transition temperature). On the contrary, the rotational diffusion of the molecular glass forming liquid and the medium viscosity remain hydrodynamically coupled even at the temperature very close to T g .Deeply supercooled liquids have spatially heterogeneous dynamics, which have been confirmed by various experiments (e.g., see Refs. 5,6,[14][15][16][17] and computer simulation studies (e.g., see . A number of computer simulation studies have indicated that the emerging spatiotemporal heterogeneity in supercooled water and other supercooled liquids has connection with the increasing violation of the SE relation with decreasing temperature. [23][24][25][26][27][28][29][30] Recently, two of us have shown that the rotation assisted translational movement of solvent water around a nonpolar solute induces translational jump-diffusion of a tracer from one solvent cage to another in supercooled water.[23]Even though the prior studies have implied the pivotal role of translational jumpdiffusion for the breakdown of the SE relation in supercooled water, a quantitative estimation of the explicit contribution of the jump-only diffusion D Jump (diffusion due to jump only motion) is still missing...

Exploring the validity of the Stokes–Einstein relation in supercooled water using nanomolecular probes

“…Combined with the agreement of the mean-squared displacement of the probe particles with Langevin dynamics (see Supplementary information (SI)), we conclude that the measured probe particle diffusion is governed by viscous flow, with negligible influence of the sort of activated hopping motion that has been associated with the anomalous self-diffusion of water 16,17 . That is, the significant contribution of jump diffusion to the total diffusion of single water molecules may account for the faster water selfdiffusion, or inversely, the lower viscosity experienced by diffusing water molecules compared to the probe particles.…”

“…Moreover, the relationship between the self-diffusion and hydrogen bond lifetime is linked to activated jumping motion of water molecules, giving rise to large angular jumps instead of continuous diffusion 15 . An increasing contribution from jump diffusion of water molecules upon cool-ing was shown in MD simulations to quantitatively describe the deviation from the Stokes-Einstein relation observed in experimental data 16,17 . This interpretation is further consistent with a growing fraction of more rigid, tetrahedral liquid structures at lower temperatures associated with LDL, in which activated motion is believed to be more significant 16,18 .…”

“…On the other hand, from the perspective that activated motion gives rise to the larger D, jump diffusion may similarly become important mainly for such small solutes, which are momentarily trapped and experience strong cage effects. Thereby, the diffusion channel is increasingly governed by the activated jump diffusion with decreasing temperature 16,17 . As a result, the jump diffusion takes control to some extent and therefore its reduction with cooling is less pronounced than the increase of viscosity.…”

Hydrogen bonds and dynamics of liquid water and alcohols

“…The persistence of the effect of the ice-like phase on the MD of water up to 298 K is confirmed by reliable extrapolations of the dependences of tres, L and tH on 1/T from the range ~250-273 K to the range 273-298 K (Figure 4). In papers [35,36,38,39,56,60], it is also believed that the excess of tres over tH and over the mean jump time of a molecule (tj) is due to a significant contribution to the kinetics of selfdiffusion of water from the MD ice-like phase. The value of tj is taken equal to L/v, where v is the average velocity of the translational motion of molecules.…”

Giant dynamic isotope effect in supercooled water

“…The factor 2 change in R h upon cooling is therefore clearly due to another cause. A recent molecular dynamics study [32] attributes the violation of SER upon cooling to the increasing role of molecular jumps in translational diffusion. When the jumps are removed, the residual diffusion due to cage trajectories of the molecules fulfills the SER.…”