Enhancement and maximum in the isobaric specific-heat capacity measurements of deeply supercooled water using ultrafast calorimetry

Unraveling the dynamic slowdown in supercooled water: The role of dynamic disorder in jump motions

When a liquid is rapidly cooled below its melting point without inducing crystallization, its dynamics slow down significantly without noticeable structural changes. Elucidating the origin of this slowdown has been a long-standing challenge. Here, we report a theoretical investigation into the mechanism of the dynamic slowdown in supercooled water, a ubiquitous yet extraordinary substance characterized by various anomalous properties arising from local density fluctuations. Using molecular dynamics simulations, we found that the jump dynamics, which are elementary structural change processes, deviate from Poisson statistics with decreasing temperature. This deviation is attributed to slow variables competing with the jump motions, i.e., dynamic disorder. The present analysis of the dynamic disorder showed that the primary slow variable is the displacement of the fourth nearest oxygen atom of a jumping molecule, which occurs in an environment created by the fluctuations of molecules outside the first hydration shell. As the temperature decreases, the jump dynamics become slow and intermittent. These intermittent dynamics are attributed to the prolonged trapping of jumping molecules within extended and stable low-density domains. As the temperature continues to decrease, the number of slow variables increases due to the increased cooperative motions. Consequently, the jump dynamics proceed in a higher-dimensional space consisting of multiple slow variables, becoming slower and more intermittent. It is then conceivable that with further decreasing temperature, the slowing and intermittency of the jump dynamics intensify, eventually culminating in a glass transition.

Liquid-liquid transition and ice crystallization in a machine-learned coarse-grained water model

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line TLL(p) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at pc = 170 ± 10 MPa and Tc = 181 ± 3 K. The TLL(p) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

A comparative review of time-resolved x-ray and electron scattering to probe structural dynamics

The structure of molecules, particularly the dynamic changes in structure, plays an essential role in understanding physical and chemical phenomena. Time-resolved (TR) scattering techniques serve as crucial experimental tools for studying structural dynamics, offering direct sensitivity to molecular structures through scattering signals. Over the past decade, the advent of x-ray free-electron lasers (XFELs) and mega-electron-volt ultrafast electron diffraction (MeV-UED) facilities has ushered TR scattering experiments into a new era, garnering significant attention. In this review, we delve into the basic principles of TR scattering experiments, especially focusing on those that employ x-rays and electrons. We highlight the variations in experimental conditions when employing x-rays vs electrons and discuss their complementarity. Additionally, cutting-edge XFELs and MeV-UED facilities for TR x-ray and electron scattering experiments and the experiments performed at those facilities are reviewed. As new facilities are constructed and existing ones undergo upgrades, the landscape for TR x-ray and electron scattering experiments is poised for further expansion. Through this review, we aim to facilitate the effective utilization of these emerging opportunities, assisting researchers in delving deeper into the intricate dynamics of molecular structures.

Potential energy landscape of a flexible water model: Equation of state, configurational entropy, and Adam-Gibbs relationship

The potential energy landscape (PEL) formalism is a tool within statistical mechanics that has been used in the past to calculate the equation of states (EOS) of classical rigid model liquids at low temperatures, where computer simulations may be challenging. In this work, we use classical molecular dynamics (MD) simulations and the PEL formalism to calculate the EOS of the flexible q-TIP4P/F water model. This model exhibits a liquid-liquid critical point (LLCP) in the supercooled regime, at (Pc = 150 MPa, Tc = 190 K, and ρc = 1.04 g/cm3) [using the reaction field technique]. The PEL-EOS of q-TIP4P/F water and the corresponding location of the LLCP are in very good agreement with the MD simulations. We show that the PEL of q-TIP4P/F water is Gaussian, which allows us to calculate the configurational entropy of the system, Sconf. The Sconf of q-TIP4P/F water is surprisingly similar to that reported previously for rigid water models, suggesting that intramolecular flexibility does not necessarily add roughness to the PEL. We also show that the Adam-Gibbs relation, which relates the diffusion coefficient D with Sconf, holds for the flexible q-TIP4P/F water model. Overall, our results indicate that the PEL formalism can be used to study molecular systems that include molecular flexibility, the common case in standard force fields. This is not trivial since the introduction of large bending/stretching mode frequencies is problematic in classical statistical mechanics. For example, as shown previously, we find that such high frequencies lead to unphysical (negative) entropy for q-TIP4P/F water when using classical statistical mechanics (yet, the PEL formalism can be applied successfully).

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress-relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamics in the deeply supercooled regime (T = 180 K), which is typically not accessible through equilibrium methods. The observed stimulated dynamic response is attributed to collective stress-relaxation as the system transitions from a jammed granular state to an elastically driven regime. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch-Williams-Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalized variance χ_T. The amplification of fluctuations is consistent with previous studies of hydrated proteins, which indicate the key role of density and enthalpy fluctuations in hydration water. Our study provides new insights into X-ray stimulated stress-relaxation and the underlying mechanisms behind spatiotemporal fluctuations in biological granular materials.

Dynamic Heterogeneity and Kovacs' Memory Effects in Supercooled Water

Understanding the properties of supercooled water is important for developing a comprehensive theory for liquid water and amorphous ices. Because of rapid crystallization for deeply supercooled water, experiments on it are typically carried out under conditions in which the temperature and/or pressure are rapidly changing. As a result, information on the structural relaxation kinetics of supercooled water as it approaches (metastable) equilibrium is useful for interpreting results obtained in this experimentally challenging region of phase space. We used infrared spectroscopy and the fast time resolution obtained by transiently heating nanoscale water films to investigate relaxation kinetics (aging) in supercooled water. When the structural relaxation of the water films was followed using a temperature jump protocol analogous to the classic experiments of Kovacs, similar memory effects were observed. In particular, after suitable aging at one temperature, water's structure displayed an extremum versus the number of heat pulses upon changing to a second temperature before eventually relaxing to a steady-state structure characteristic of that temperature. A random double well model based on the idea of dynamic heterogeneity in supercooled water accounts for the observations.

Liquid-Liquid Criticality in TIP4P/2005 and Three-State Models of Water

Molecular dynamics simulations leading to the isothermal compressibility, the isobaric thermal expansivity, and the isobaric heat capacity of TIP4P/2005 water are found to be consistent with the coordinates of its second, liquid-liquid critical point reported recently by Debenedetti et al. [ Science 2020, 369, 289-292]. In accord with the theory of critical phenomena, we encounter that the rise in the magnitude of these response functions as temperature is lowered is especially marked along the critical isochore. Furthermore, response-function ratios provide a test for thermodynamic consistency at the critical point and manifest nonuniversal features sharply distinguishing liquid-liquid from standard gas-liquid criticality. The whole pattern of behavior revealed by simulations is qualitatively the same as the one of a three-state Ising model of water exhibiting a low-temperature liquid-liquid critical point. Exact solutions for the two-state components of such a three-state model are also provided.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

The Swiss Light Source and SwissFEL at the Paul Scherrer Institute

At the Paul Scherrer Institute, two electron accelerator-based photon sources are in operation, namely a synchrotron source, the swiss light source (SLS), and an X-ray free-electron laser, SwissFEL. SLS has been operational since 2001 and SwissFEL since 2017. In this time, unique and world-leading scientific programs and methods have developed from the SLS and the SwissFEL in fields as diverse as macromolecular biology, chemical and physical sciences, imaging, and the electronic structure and behaviour of novel and complex materials. To continue the success, a major upgrade of SLS, the SLS2.0 project, is ongoing and at SwissFEL further endstations are under construction.

Liquid Water: A Single Approach to Its Two Continuous Phase Transitions

In this paper, we show that both continuous phase transitions of liquid water, the liquid-gas and the liquid-liquid, can be articulated within a single thermodynamic analytical formalism. This result follows from a combination of the two-liquid model (TLM), recently confirmed for water, with the idea of a thermal-dependent excluded volume, v_e, concept introduced by van der Waals, in his famous state equation. Starting from the fundamentals of thermodynamics, it will be shown that the TLM naturally leads to the idea of an extensive thermal-dependent v_e that acts as a parameter of the sample thermodynamic potentials. This procedure effectively separates the thermodynamics of the system into two parts: the first concerns the clusters' thermodynamics, taken as wandering particles, and the second concerns the thermal behavior of its internal structure (geometry and number of particles). From this result, we demonstrate that the condition of mechanical instability leads to not one but two critical points, each happening in one of the above-described parts of the system.

Refractive Index of Supercooled Water Down to 230.3 K in the Wavelength Range between 534 and 675 nm

Knowledge of the refractive index of water in the deeply supercooled metastable liquid state is important, for example, for an accurate description of optical reflection and refraction processes occurring in clouds. However, a measurement of both the temperature and wavelength dependence of the refractive index under such extreme conditions is challenging. Here, we employ Raman spectroscopy in combination with microscopic water jets in vacuum to obtain the refractive index of supercooled water to a lowest temperature of 230.3 K. While our approach is based on the analysis of Mie resonances in Raman spectra measured by using a single excitation wavelength at 532 nm, it allows us to obtain the refractive index in a wide visible wavelength range from 534 to 675 nm. Because of a direct link between the refractive index and density of water, our results provide a promising approach to help improve our understanding of water's anomalous behavior.

Liquid-Liquid Transition in Water from First Principles

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

Manifestations of the structural origin of supercooled water’s anomalies in the heterogeneous relaxation on the potential energy landscape

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models—based on the assumption of the existence of two types of competing local states (or, structures) in liquid water—have been extremely successful in describing water’s thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a predefined structural order parameter-free approach to unambiguously identify two types of competing local states—entropically and energetically favored—with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water’s thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

Revealing the three-component structure of water with principal component analysis (PCA) of X-ray spectra

Combining principal component analysis (PCA) of X-ray spectra with MD simulations, we experimentally reveal the existence of three basic components in water. These components exhibit distinct structures, densities, and temperature dependencies. Among the three, the two major components correspond to the low-density liquid (LDL) and the high-density liquid (HDL) predicted by the two-component model, and the third component exhibits a unique 5-hydrogen-bond configuration with ultra-high local density. As the temperature increases, the LDL component decreases and the HDL component increases, while the third component varies non-monotonically with a peak around 20 °C to 30 °C. The 3D structure of the third component is further illustrated as the uniform distribution of five hydrogen-bonded neighbors on a spherical surface. Our study reveals experimental evidence for water's possible three-component structure, which provides a fundamental basis for understanding water's special properties and anomalies.

Water's Unusual Thermodynamics in the Realm of Physical Chemistry

While it is known since the early work by Edsall, Frank and Evans, Kauzmann, and others that the thermodynamics of solvation of nonpolar solutes in water is unusual and has implications for the thermodynamics of protein folding, only recently have its connections with the unusual temperature dependence of the density of solvent water been illuminated. Such density behavior is, in turn, one of the manifestations of a nonstandard thermodynamic pattern contemplating a second, liquid-liquid critical point at conditions of temperature and pressure at which water exists as a deeply supercooled liquid. Recent experimental and computational work unambiguously points toward the existence of such a critical point, thereby providing concrete answers to the questions posed by the 1976 pioneering experiments by Speedy and Angell and the associated "liquid-liquid transition hypothesis" posited in 1992 by Stanley and co-workers. Challenges of this phenomenology to the branch of Statistical Mechanics remain.

Fluorescent molecular rotor probes nanosecond viscosity changes

Viscosity is a key property of liquids, but it is difficult to measure in short-lived, metastable samples due to the long measuring times required by conventional rheology. Here, we show how this problem can be solved by using fluorescent molecular rotors. The excited-state fluorescence decay rate of these molecules is sensitive to the viscosity of their local environment, and by combining pulsed laser excitation with time-resolved fluorescence detection, we can measure viscosities with a time resolution of a few ns. We demonstrate this by measuring in real time the viscosity change in glycerol induced by a nanosecond temperature jump. This new approach makes it possible to measure the viscosity of extremely short-lived states of matter.

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

Evidence of a liquid-liquid phase transition in H[Formula: see text]O and D[Formula: see text]O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H[Formula: see text]O and D[Formula: see text]O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density [Formula: see text], isothermal compressibility [Formula: see text], and self-diffusion coefficients D(T) of H[Formula: see text]O and D[Formula: see text]O are in excellent agreement with available experimental data; the isobaric heat capacity [Formula: see text] obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H[Formula: see text]O and D[Formula: see text]O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H[Formula: see text]O and D[Formula: see text]O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H[Formula: see text]O, from PIMD simulations, is located at [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D[Formula: see text]O is estimated to be [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of [Formula: see text] for D[Formula: see text]O and, particularly, H[Formula: see text]O suggest that improved water models are needed for the study of supercooled water.

Is It Possible to Follow the Structural Evolution of Water in "No-Man's Land" Using a Pulsed-Heating Procedure?

The anomalous increase in compressibility and heat capacity of supercooled water has been attributed to its structural transformation of into a four-coordinated liquid. Experiments revealed that κ_T and C_p peak at T_W^thermo ≈ 229 K [Kim et al. Science 2017, 358, 1589; Pathak et al. Proc. Natl. Acad. Sci. 2021, 118, e2018379118]. Recently, a pulsed heating procedure (PHP) was employed to interrogate the structure of water, reporting a steep increase in tetrahedrality around T_W^PHP = 210 ± 3 K [Kringle et al. Science 2020, 369, 1490]. This discrepancy questions whether water structure and thermodynamics are decoupled, or if the shift in T_W is an artifact of PHP. Here we implement PHP in molecular simulations. We find that the stationary states captured at the bottom of the pulse are not representative of the thermalized liquid or its inherent structure. Our analysis reveals a temperature-dependent distortion that shifts T_W^PHP to ∼20 K below T_W^thermo. We conclude that 2 orders of magnitude faster rates are required to sample water's inherent structure with PHP.

Heterogeneous Ice Growth in Micron-Sized Water Droplets Due to Spontaneous Freezing

Understanding how ice nucleates and grows into larger crystals is of crucial importance for many research fields. The purpose of this study was to shed light on the phase and structure of ice once a nucleus is formed inside a metastable water droplet. Wide-angle X-ray scattering (WAXS) was performed on micron-sized droplets evaporatively cooled to temperatures where homogeneous nucleation occurs. We found that for our weak hits ice grows more cubic compared to the strong hits that are completely hexagonal. Due to efficient heat removal caused by evaporation, we propose that the cubicity of ice at the vicinity of the droplet’s surface is higher than for ice formed within the bulk of the droplet. Moreover, the Bragg peaks were classified based on their geometrical shapes and positions in reciprocal space, which showed that ice grows heterogeneously with a significant population of peaks indicative of truncation rods and crystal defects. Frequent occurrences of the (100) reflection with extended in-planar structure suggested that large planar ice crystals form at the droplet surface, then fracture into smaller domains to accommodate to the curvature of the droplets. Planar faulting due to misaligned domains would explain the increased cubicity close to the droplet surface.

Anomalous temperature dependence of the experimental x-ray structure factor of supercooled water

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å^-1, which covered the principal doublet of the x-ray structure factor of water. The oxygen-oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen-oxygen structure factor (q₂). We found that q₂ exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q₂ shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen-oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

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.

Hydrophilic and Hydrophobic Effects on the Structure and Themodynamic Properties of Confined Water: Water in Solutions

NMR spectroscopy is used in the temperature range 180–350 K to study the local order and transport properties of pure liquid water (bulk and confined) and its solutions with glycerol and methanol at different molar fractions. We focused our interest on the hydrophobic effects (HE), i.e., the competition between hydrophilic and hydrophobic interactions. Nowadays, compared to hydrophilicity, little is known about hydrophobicity. Therefore, the main purpose of this study is to gain new information about hydrophobicity. As the liquid water properties are dominated by polymorphism (two coexisting liquid phases of high and low density) due to hydrogen bond interactions (HB), creating (especially in the supercooled regime) the tetrahedral networking, we focused our interest to the HE of these structures. We measured the relaxation times (T1 and T2) and the self-diffusion (DS). From these times, we took advantage of the NMR property to follow the behaviors of each molecular component (the hydrophilic and hydrophobic groups) separately. In contrast, DS is studied in terms of the Adam–Gibbs model by obtaining the configurational entropy (Sconf) and the specific heat contributions (CP,conf). We find that, for the HE, all of the studied quantities behave differently. For water–glycerol, the HB interaction is dominant for all conditions; water–methanol, two different T-regions above and below 265 K are observable, dominated by hydrophobicity and hydrophilicity, respectively. Below this temperature, where the LDL phase and the HB network develops and grows, with the times and CP,conf change behaviors leading to maxima and minima. Above it, the HB becomes weak and less stable, the HDL dominates, and hydrophobicity determines the solution.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water

We perform path-integral molecular dynamics (PIMD) simulations of H₂O and D₂O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H₂O and D₂O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient α_P(T), isothermal compressibility κ_T(T), isobaric heat capacity C_P(T), and static dielectric constant ε(T). While these properties are in excellent [α_P(T) and κ_T(T)] or semi-quantitative agreement [C_P(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in C_P(T) and κ_T(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κ_T(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in C_P(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H₂O and D₂O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with C_P(T), D(T), and structural properties being the only (expected) exceptions.