Importance of Solvents’ Translational–Rotational Coupling for Translational Jump of a Small Hydrophobic Solute in Supercooled Water

Enhanced fluidity of water in superhydrophobic nanotubes: estimating viscosity using jump-corrected confined Stokes-Einstein approach

Accurately predicting the viscosity of water confined within nanotubes is vital for various technological applications. Traditional methods have failed in this regard, necessitating a novel approach. We introduced the jump-corrected confined Stokes-Einstein (JCSE) method and now employ the same to estimate the viscosity and diffusion in superhydrophobic nanotubes. Our study covers a temperature range of 230-300 K and considers three nanotube diameters. Results show that water inside superhydrophobic nanotubes exhibits a significantly lower viscosity and higher diffusion than those inside hydrophobic nanotubes. Narrower nanotubes and lower temperatures accentuate these effects. Furthermore, water inside superhydrophobic nanotubes display a lower viscosity than bulk water, with the difference increasing at lower temperatures. This reduction is attributed to weaker water-water interactions caused by a lower water density in the interfacial region. These findings highlight the importance of interfacial water density and its influence on nanotube viscosity, shedding light on nanoscale fluid dynamics and opening avenues for diverse applications.

Non-monotonic composition dependence of the breakdown of Stokes-Einstein relation for water in aqueous solutions of ethanol and 1-propanol: explanation using translational jump-diffusion approach

A series of experimental and simulation studies examined the validity of the Stokes-Einstein relationship (SER) of water in binary water/alcohol mixtures of different mixture compositions. These studies revealed a strong non-monotonic composition dependence of the SER with maxima at the specific alcohol mole fraction where the non-idealities of the thermodynamic and transport properties are observed. The translational jump-diffusion (TJD) approach elucidated the breakdown of the SER in pure supercooled water as caused by the jump translation of molecules. The breakdown of SER in the supercooled water/methanol binary mixture was successfully explained using the same TJD approach. To further generalize the picture, here we focus on the non-monotonic composition dependence of SER breakdown of water in two water/alcohol mixtures (water/ethanol and water/propanol) for a broad temperature range. In agreement with previous studies, maximum breakdown of SER is observed for the mixture with alcohol mole fraction x = 0.2. Diffusion of the water molecules at the maximum SER breakdown point is largely contributed by jump-diffusion. The residual-diffusion, obtained by subtracting the jump-diffusion from the total diffusion, approximately follows the SER for different compositions and temperatures. We also performed hydrogen (H-)bond dynamics and observed that the contribution of jump-diffusion is proportional to the total free energy of activation of breaking all H-bonds that exist around a molecule. This study, therefore, suggests that the more a molecule is trapped by H-bonding, the more likely it is to diffuse through the jump-diffusion mechanism, eventually leading to an increasing degree of SER breakdown.

Non-Markovian rate theory on a multidimensional reaction surface: Complex interplay between enhanced configuration space and memory

A theory of barrier crossing rate on a multidimensional reaction energy surface is presented. The theory is a generalization of the earlier theoretical schemes to higher dimensions, with the inclusion of non-Markovian friction along both the reactive and the nonreactive coordinates. The theory additionally includes the bilinear coupling between the reactive and the nonreactive modes at the Hamiltonian level. Under suitable conditions, we recover the rate expressions of Langer and Hynes and establish a connection with the rate treatment of Pollak. Within the phenomenology of generalized Langevin equation description, our formulation provides an improvement over the existing ones because we explicitly include both the non-Markovian effects along the reaction coordinate and the bilinear coupling at the Hamiltonian level. At intermediate-to-large friction, an increase in dimensionality by itself tends to reduce the rate, while the inclusion of the memory effects increases the rate. The theory predicts an increase in rate when off-diagonal friction terms are included. We present a model calculation to study isomerization of a stilbene-like molecule using the prescription of Hochstrasser and co-workers on a two-dimensional reaction energy surface, employing Zwanzig–Bixon hydrodynamic theory of frequency-dependent friction. The calculated rate shows a departure from the predictions of Langer’s theory and also from the two-dimensional transition state theory.

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

The breakdown of Stokes-Einstein relation in liquid water is one of the many anomalies that take place upon cooling and indicates the decoupling of diffusion and viscosity. It is hypothesized that these anomalies manifest due to the appearance of nanometer-scale spatial fluctuations, which become increasingly pronounced in the supercooled regime. Here, we explore the validity of the Stokes-Einstein relation in supercooled water using nanomolecular probes. We capture the diffusive dynamics of the probes using dynamic light scattering and target dynamics at different length scales by varying the probe size, from ≈100 nm silica spheres to molecular-sized polyhydroxylated fullerenes (≈1 nm). We find that all the studied probes, independent of size, display similar diffusive dynamics with an Arrhenius activation energy of ≈23 kJ mol^-1. Analysis of the diffusion coefficient further indicates that the probes, independent of their size, experience similar dynamic environment, which coincides with the macroscopic viscosity, while single water molecules effectively experience a comparatively lower viscosity. Finally, we conclude that our results indicate that the Stokes-Einstein relation is preserved for diffusion of probes in supercooled water T ≥ 260 K with size as small as ≈1 nm.

Breakdown of the Stokes-Einstein relation in supercooled water: the jump-diffusion perspective

Although water is the most ubiquitous liquid it shows many thermodynamic and dynamic anomalies. Some of the anomalies further intensify in the supercooled regime. While many experimental and theoretical studies have focused on the thermodynamic anomalies of supercooled water, fewer studies explored the dynamical anomalies very extensively. This is due to the intricacy of the experimental measurement of the dynamical properties of supercooled water. Violation of the Stokes-Einstein relation (SER), an important relation connecting the diffusion of particles with the viscosity of the medium, is one of the major dynamical anomalies. In absence of experimentally measured viscosity, researchers used to check the validity of SER indirectly using average translational relaxation time or α-relaxation time. Very recently, the viscosity of supercooled water was accurately measured at a wide range of temperatures and pressures. This allowed direct verification of the SER at different temperature-pressure thermodynamic state points. An increasing breakdown of the SER was observed with decreasing temperature. Increasing pressure reduces the extent of breakdown. Although some well-known theories explained the above breakdown, a detailed molecular mechanism was still elusive. Recently, a translational jump-diffusion (TJD) approach has been able to quantitatively explain the breakdown of the SER in pure supercooled water and an aqueous solution of methanol. The objective of this article is to present a detailed and state-of-the-art analysis of the past and present works on the breakdown of SER in supercooled water with a specific focus on the new TJD approach for explaining the breakdown of the SER.

Breakdown of the Stokes-Einstein Relation in Supercooled Water/Methanol Binary Mixtures: Explanation Using the Translational Jump-Diffusion Approach

A recent experiment has directly checked the validity of the Stokes-Einstein (SE) relation for pure water, pure methanol, and their binary mixtures of three different compositions at different temperatures. The effect of composition on the nature of breakdown of the SE relation is interesting. While in the majority of the systems, an increasing SE breakdown is observed with decreasing temperature, the breakdown is already significant at higher temperatures for the equimolar mixture. Violations of the SE relation in pure supercooled water at different temperatures and pressures have been previously explained using the translational jump-diffusion (TJD) approach, which provides a fundamental molecular basis, by directly connecting the SE breakdown with jump-diffusion of the molecules. We have used the same TJD approach for explaining the SE breakdown for the methanol/water binary mixtures of compositions studied in the experiment over a wide range of temperatures between 220 K and 300 K. We have understood that the jump-diffusion is the key responsible factor for the SE breakdown. The maximum jump-diffusion contribution gives rise to the early SE breakdown observed for the equimolar mixture observed in the experiment. This study, therefore, provides molecular insight into the SE breakdown for the supercooled water/methanol binary mixture, as found in the experiment.

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

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.