Understanding the Origin of the Breakdown of the Stokes–Einstein Relation in Supercooled Water at Different Temperature–Pressure Conditions

Abstract

A recent experiment has measured the viscosity of water down to approximately 244 K and up to 300 MPa. The correct viscosity and translational diffusivity data at various temperature–pressure (T–P) state points allowed for checking the validity of the Stokes–Einstein (SE) relation, which accounts for the coupling between translational self-diffusion and medium viscosity. The diffusion–viscosity decoupling increases with decreasing temperature, but the increasing pressure reduces the extent of the decoupling. Earlier simulation studies explained the breakdown of the SE relation in terms of the location of the Widom line, emanating from the liquid–liquid critical point (LLCP). Although these studies made a significant contribution to the current understanding of the above phenomena, a detailed molecular picture is still lacking. Recently, our group has explained the diffusion–viscosity decoupling from a jump-diffusion perspective. The jump-diffusion coefficient, emanating from the jump translation of water molecules, is calculated using a quantitative approach for different temperatures at ambient pressure. It has been observed that jump-diffusion is the key factor for diffusion–viscosity decoupling in supercooled water. The same method is adopted in the present work to estimate the jump-diffusion coefficient for different T–P state points and, thereby, explains the role of jump-diffusion for the different extents of the SE relation breakdown at different pressures. The residual diffusion coefficient, the other component of the total diffusion that originates from small step displacement and that is calculated by subtracting the jump-diffusion coefficient from the total diffusion, is seen to be fairly coupled to the viscosity at the entire range of temperature and pressure. Furthermore, we have calculated the average number of H-bonds per water molecule and the tetrahedral order for different T–P state points and investigated an approximate correlation between the average local structure and the contribution of the jump-diffusion to the total diffusion of water. This study, therefore, puts forward a new perspective for explaining the SE relation breakdown in supercooled water under different pressure conditions.

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 .…”

“…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 . Hence, the dynamic transition manifested by the fragile-to-strong crossover and the violation of Stokes-Einstein relation in supercooled water are likely highly interconnected, and both linked to spatially heterogeneous dynamics at microscopic level.…”

“…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.…”

Microscopic structural features of water in aqueous–reline mixtures of varying compositions

“…73 Later, Dubey et al correlate the variation of temperature and contribution of jump-diffusion coefficient with that of the average tetrahedrality of water, which shows a decreasing average tetrahedral ordering with increasing temperature, while the contribution of jump-diffusion coefficient increases linearly with that of the average tetrahedral parameter. 74 The effect of urea on the water structure is arguable and how a bulky molecule like choline affect the structure of water is still largely unknown. In this investigation, by considering a range of aqueous ternary solutions with urea and choline chloride in 2:1 molar ratio, we have explored the role of the individual constituents in making/breaking the tetrahedral framework of water.…”