New Effective Method for Quantitative Analysis of Diffusion Jumps, Applied in Molecular Dynamics Simulations of Small Molecules Dispersed in Short Chain Systems

Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane

A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.

Difference in "Supercooling" Affinity between (Acetamide + Na/KSCN) Deep Eutectics: Reflections in the Simulated Anomalous Motions of the Constituents and Solution Microheterogeneity Features

Deep depression of freezing points of ionic amide deep eutectic solvents (DESs) is known to exhibit a significant dependence on the identity of ions present in those systems and the nature of the functional group attached to the host amide. This deep depression of the freezing point is sometimes termed as "supercooling". For (acetamide + electrolyte) DESs, experiments have revealed signatures of ion-dependent spatiotemporal heterogeneity features. The focus of this work is to provide microscopic explanations of these experimentally observed macroscopic system properties in terms of particle jumps and insights about the origin of the cation dependence. For this purpose, extensive molecular dynamics simulations have been performed employing (acetamide + Na/KSCN) deep eutectics as representative ionic systems at 303, 318, 333, and 348 K. The individual translational motions of acetamide and the ions are followed, and their connections to solution heterogeneity are explored. The center-of-mass motion for Na⁺ has been found to be more anomalous than that for K⁺. This difference corroborates well with experimental reports on heterogeneous relaxations in these systems. Simulated viscosity coefficients and dynamic heterogeneity features also reflect this difference. Moreover, simulated reorientational relaxations of acetamide molecules in these ionic DESs suggest that a Na⁺-containing DES is more heterogeneous than the corresponding K⁺-containing system. Estimated void and neck distributions for acetamide molecules differ as the alkali metal ions differ. In brief, this study provides a detailed microscopic view of the cation dependence of the microheterogeneous relaxation dynamics of these DESs reported repeatedly by different experiments.

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.

Translational Jump-Diffusion of Hydroxide Ion in Anion Exchange Membrane: Deciphering the Nature of Vehicular Diffusion

Earlier, ab initio and reactive force-field-based molecular dynamics (MD) simulation studies suggested an overwhelming contribution of the vehicular diffusion in the total diffusion of hydroxide ions rather than structural diffusion. But does the vehicular diffusion occur via small-step displacement? This question is important to have an understanding of the real characteristics of vehicular diffusion. To answer this question, we perform a classical molecular dynamics simulation of a system containing a hydroxide ion exchange membrane polymer and hydroxide ion at different hydration levels and temperatures using the same molecular force field (Dubey, V. Chem. Phys. Lett. 2020, 755, 137802), which successfully captured the microscopic structure and dynamics of the system. We use the translational jump-diffusion approach, used previously in supercooled water for understanding the origin of breakdown of the Stokes-Einstein relation, to calculate the jump-diffusion coefficient of hydroxide ion and water in the anion exchange membrane. We have seen a significant role of hydration level and temperature in the mechanism of vehicular diffusion. In overhydrated membrane, both hydroxide ions and water molecules diffuse via both small- and large-step displacement. With decreasing hydration level and temperature, the diffusion is increasingly governed by the jump-diffusion mechanism. The larger contribution of jump-diffusion comes from the stronger caging of the diffusing species by the solvent at lower hydration levels and temperature. These results, therefore, suggest that the hydration level and temperature of the hydroxide ion exchange membrane determine the detailed mechanism of the vehicular diffusion of hydroxide ion, especially whether the diffusion follows hydrodynamics or not.

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.

Nanocrystal diffusion in a liquid thin film observed by in situ transmission electron microscopy

We have directly observed motion of inorganic nanoparticles during fluid evaporation using a transmission electron microscope. Tracking real-time diffusion of both spherical (5-15 nm) and rod-shaped (5 x 10 nm) gold nanocrystals in a thin film of water-15% glycerol reveals complex movements, such as rolling motions coupled to large-step movements and macroscopic violations of the Stokes-Einstein relation for diffusion. As drying patches form during the final stages of evaporation, particle motion is dominated by the nearby retracting liquid front.