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Nanoscale confinement of molecules in a fluid can result in enhanced viscosity, local fluidic order, or collective motion. Confinement also affects ion transport and/or the rate and equilibrium concentration in a chemical reaction, all of which makes it the subject of broad interest. Studying these effects, however, is notoriously difficult, mainly due to the lack of experimental methods with the required sensitivity and spatial or time resolution. Here we leverage shallow nitrogen-vacancy (NV) centers in diamond to probe the dynamics of room-temperature water molecules entrapped within ~6-nm-tall channels formed between the diamond crystal and a suspended hexagonal boron nitride (hBN) flake. NV-enabled nuclear magnetic resonance measurements of confined water protons reveal a much reduced H2O self-diffusivity, orders of magnitude lower than in bulk water. We posit the slow dynamics stem from the accumulation of photogenerated carriers at the interface and trapped fluid, a notion we support with the help of molecular dynamics modeling. Our results provide feedback for theories describing interfacial water, and lay out a route for investigating other fluids under confinement.

Recent experiments and theoretical studies strongly indicate that water exhibits a liquid-liquid phase transition (LLPT) in the supercooled domain. An open question is how the LLPT of water can affect the properties of aqueous solutions. Here, we study the structural and thermodynamic properties of supercooled glycerol-water microdroplets at dilute conditions ($\chi_g=3.2~\%$ glycerol mole fraction). The combination of rapid evaporative cooling with ultrafast X-ray scattering allows us to outrun crystallization and gain access to the deeply supercooled regime down to $T=229.3$ K. We find that the density fluctuations of the glycerol-water solution or, equivalently, its isothermal compressibility, $\kappa_T$, increases upon cooling. This is confirmed by molecular dynamics simulations, which indicate that the presence of glycerol shifts the temperature of maximum $\kappa_T$ from $T=230$ K in pure water down to $T=223$ K in the solution. Our findings elucidate the interplay between the complex behavior of water, including its LLPT, and the properties of aqueous solutions at low temperatures, which can have practical consequences in cryogenic biological applications and cryopreservation techniques.

A recent experiment [K. H. Kim, et al., Science 370, 978 (2020)] showed that it may be possible to detect a liquid-liquid phase transition (LLPT) in supercooled water by subjecting high density amorphous ice (HDA) to ultrafast heating, after which the sample reportedly undergoes spontaneous decompression from a high density liquid (HDL) to a low density liquid (LDL) via a first-order phase transition. Here we conduct computer simulations of the ST2 water model, in which a LLPT is known to occur. We subject various HDA samples of this model to a heating and decompression protocol that follows a thermodynamic pathway similar to that of the recent experiments. Our results show that a signature of the underlying equilibrium LLPT can be observed in a strongly out-of-equilibrium process that follows this pathway despite the very high heating and decompression rates employed here. Our results are also consistent with the phase diagram of glassy ST2 water reported in previous studies., Comment: 14 pages, 12 figures

The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) using computer simulations of the TIP4P/2005 molecular model of water. We find that the properties of the PEL sampled by the system during the LDA-HDA transformation exhibit anomalous behavior. In particular, at conditions where the change in density during the LDA-HDA transformation is approximately discontinuous, reminiscent of a first-order phase transition, we find that (i) the inherent structure (IS) energy, $e_\text{IS}(V)$, is a concave function of the volume, and (ii) the IS pressure, $P_\text{IS}(V)$, exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a non-monotonic function of $V$. In agreement with previous studies, our work suggests that conditions (i) and (ii) are necessary (but not sufficient) signatures of the PEL for the LDA-HDA transformation to be reminiscent of a first-order phase transition. We also find that one can identify two different regions of the PEL, one associated to LDA and another to HDA. Our computer simulations are performed using a wide range of compression/decompression and cooling rates. In particular, our slowest cooling rate (0.01 K/ns) is within the experimental rates employed in hyperquenching experiments to produce LDA. Interestingly, the LDA-HDA transformation pressure that we obtain at $T=80$ K and at different rates extrapolates remarkably well to the corresponding experimental pressure., Comment: Manuscript and Supplementary Material

We employ classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice (I$h$) and low-density amorphous (LDA) ice at low temperatures. In both cases, the system transforms to high-density amorphous ice (HDA) via a first-order-like phase transition. We employ a sensitive local order metric (LOM) [Martelli et. al., Phys. Rev. B, 97, 064105 (2018)], that can discriminate among different crystalline and non crystalline ice structures and is based on the positions of the oxygen atoms in the first and/or second hydration shell. Our results confirm that LDA and HDA are indeed amorphous, i.e., they lack of polydispersed ice domains. Interestingly, HDA contains a small number of domains that are reminiscent of the unit cell of ice IV, although the hydrogen-bond network (HBN) of these domains differ from the HBN of ice IV. The presence of ice IV-like domains provides some support to the hypothesis that HDA could be the result of a detour on the HBN rearrangement along the I$h$-to-ice IV pressure induced transformation. Both nonequilibrium LDA-to-HDA and I$h$-to-HDA transformations are two-steps processes where a small distortion of the HBN first occurs at low pressures and then, a sudden, extensive re-arrangement of hydrogen bonds at the corresponding transformation pressure follows. Interestingly, the I$h$-to-HDA and LDA-to-HDA transformations occur when LDA and I$h$ have similar local order, as quantified by the site-averaged LOMs. Since I$h$ has a perfect tetrahedral HBN, while LDA does not, it follows that higher pressures are needed to transform I$h$ into HDA than that for the conversion of LDA to HDA. In correspondence with both first-order-like phase transitions, the samples are composed of a large HDA cluster that percolates within the I$h$/LDA samples.

Experiments and computer simulations of the transformations of amorphous ices display different behavior depending on sample preparation methods, and on the rates of change of temperature and pressure to which samples are subjected. In addition to these factors, simulation results also depend strongly on the chosen water model. Using computer simulations of the ST2 water model, we study how the sharpness of the compression-induced transition from low-density amorphous ice (LDA) to high-density amorphous ice (HDA) is influenced by the preparation of LDA. By studying LDA samples prepared using widely different procedures, we find that the sharpness of the LDA-to- HDA transformation is correlated with the depth of the initial LDA sample in the potential energy landscape (PEL), as characterized by the inherent structure energy. Our results show that the complex phenomenology of the amorphous ices reported in experiments and computer simulations can be understood and predicted in a unified way from a knowledge of the PEL of the system., Comment: 21 pages, 14 figures

We investigate the large-scale structure of amorphous ices and transitions between their different forms by quantifying their large-scale density fluctuations. Specifically, we simulate the isothermal compression of low-density amorphous ice (LDA) and hexagonal ice (Ih) to produce high-density amorphous ice (HDA). Remarkably, both HDA and LDA are nearly hyperuniform, meaning that they are characterized by an anomalous suppression of large-scale density fluctuations. By contrast, in correspondence with both non-equilibrium phase transitions to HDA, the presence of structural heterogeneities strongly suppresses the hyperuniformity and, remarkably, the system becomes hyposurficial (devoid of "surface-area" fluctuations). Our investigation challenges the largely accepted "frozen-liquid" picture, which views glasses as structurally arrested liquids. Beyond implications for water, our findings enrich our understanding of the structural transformations that occur in glasses with varying pressures.

The potential energy landscape (PEL) formalism is a valuable approach within statistical mechanics for describing supercooled liquids and glasses. Here we use the PEL formalism and computer simulations to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) at different temperatures. We employ the ST2 water model for which the LDA-HDA transformations are remarkably sharp, similar to what is observed in experiments, and reminiscent of a first-order phase transition. Our results are consistent with the view that LDA and HDA configurations are associated with two distinct regions (megabasins) of the PEL that are separated by a potential energy barrier. At higher temperature, we find that low-density liquid (LDL) configurations are located in the same megabasin as LDA, and that high-density liquid (HDL) configurations are located in the same megabasin as HDA. We show that the pressure-induced LDL-HDL and LDA-HDA transformations occur along paths that interconnect these two megabasins, but that the path followed by the liquid is different than the path followed by the amorphous solid. At higher pressure, we also study the liquid-to-ice-VII first-order phase transition, and find that the behavior of the PEL properties across this transition are qualitatively similar to the changes found during the LDA-HDA transformation. This similarity supports the interpretation that the LDA-HDA transformation is a first-order-like phase transition between out-of-equilibrium states., Comment: 29 pages, 8 figures

We perform molecular dynamics simulations of a well-known water model (the TIP5P pair potential) and a simple liquid model (a two-scale repulsive ramp potential) to compare the regions of anomalous behavior in their phase diagrams. We select the parameters of the ramp potential by mapping it to an effective pair potential derived from the TIP5P model. We find that the regions of anomalous behavior in the phase diagrams of both systems can be mapped onto each other if (i) pressure $P$ and temperature $T$ are replaced by $T-T_{C}$ and $P-P_{C}$, respectively, where $(T_{C},P_{C})$ are the coordinates of the liquid-liquid critical point of the corresponding system; and (ii) a single ramp particle corresponds to two TIP5P molecules. We present heuristic arguments supporting point (ii). We also argue that the water-like anomalies in the ramp potential are due to the ability of the particles to reproduce, upon compression or heating, the migration of water molecules from the second shell to its first shell.

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations using molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE and SED relations break down at low temperature. To explore the relationship between these breakdowns and dynamical heterogeneities (DH), we also calculate the SE and SED relations for subsets of the 7% ``fastest'' and 7% ``slowest'' molecules. We find that the SE and SED relations break down in both subsets, and that the breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in contrast with the view where only the most mobile molecules are the origin of the breakdown of the SE and SED relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED relations in both subsets of molecules are replaced with ``fractional'' SE and SED relations, $D_t\sim(\tau/T)^{-\xi_t}$ and $D_r\sim(\tau/T)^{-\xi_r}$ where $\xi_t\approx0.84<1$ and $\xi_r\approx0.75<1$. We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both fastest and slowest subsets of molecules. We also find that when the decoupling increases, upon cooling, the probability of a molecule being classified as both translationally and rotationally fastest also increases. To study the effect of time scale for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both the decoupling and SE and SED breakdowns are originated at the time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DH are more relevant.

We perform molecular dynamics simulation of water using the TIP5P model to quantify structural order in both the first shell (defined by four nearest neighbors)and second shell (defined by twelve next-nearest neighbors) of a central water molecule. We find the anomalous decrease of orientational order upon compression occurs in both shells, but the anomalous decrease of translational order upon compression occurs {\it mainly in the second shell}. The decreases of translational and orientational orders upon compression ("structural anomaly") are thus correlated only in the second shell. Our findings quantitatively confirm the qualitative idea that the thermodynamic, dynamic and structural anomalies of water are related to changes in the second shell upon compression., Comment: 12 pages, 5 figures

We perform systematic molecular dynamics simulations of water confined between two nanoscale plates at T=300 K. We investigate the effect of pressure (-0.15 GPa <= P <= 0.2 GPa) and plate separation (0.4 nm <= d <= 1.6 nm) on the phase behavior of water when the plates are either hydrophobic or hydrophilic. When water is confined between hydrophobic plates, capillary evaporation occurs between the plates at low enough P. The threshold value of d at which this transition occurs decreases with P (e.g., 1.6 nm at P ~ -0.05 GPa; 0.5 nm at P \~ 0.1 GPa), until, at high P, no capillary evaporation occurs. For d ~ 0.6 nm and P >= 0.1 GPa, the system crystallizes into a bilayer ice. A P-d phase diagram showing the vapor, liquid, and bilayer ice phases is proposed. When water is confined by hydrophilic (hydroxylated silica) plates, it remains in the liquid phase at all P and d studied. Interestingly, we observe, for this case, that even at the P at which bulk water cavitates, the confined water remains in the liquid state. We also study systematically the state of hydration at different P for both kinds of plates. For the range of conditions studied here, we find that in the presence of hydrophobic plates the effect of P is to enhance water structure and to push water molecules toward the plates. The average orientation of water molecules next to the hydrophobic plates does not change upon pressurization. In contrast, in the presence of hydrophilic plates, water structure is insensitive to P. Hence, our results suggest that upon pressurization, hydrophobic plates behave as `soft' surfaces (in the sense of accommodating pressure-dependent changes in water structure) while hydrophilic walls behave as `hard' surfaces., Comment: accepted for publication in Phys. Rev. E. Figs. 1, 3, 4, and 6 are in low resolution to avoid large fig. files

We perform molecular dynamics simulations to investigate the relationship between structural order and water-like dynamic and thermodynamic anomalies in spherically-symmetric potentials having either one or two characteristic length scales. %The first potential has only one length scale which is the diameter of the ramp %without the hard core, and the second potential has two length scales: one is the %diameter of a ramp(softcore) and another one is the diameter of a %hard core with a ratio of 1.76. Structural order is characterized by translational and orientational order parameters. %analogous to those used in previous cases for water and %silica.Only the two-scale ramp potential exhibits properties %remarkably similar to those found for water and silica regarding the %relationship between structural order, dynamic anomalies, and thermodynamic %anomalies. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) water-like structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the water-like relationship between structural order and anomalies is related to the presence of two different length scales in the potential., Comment: 12 pages, 5 figures

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically-symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, $\lambda$. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0\leq\lambda<6/7$. As in water, the regions where these anomalies occur are nested domes in the ($T, \rho$) or ($T, P$) planes, with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters ($t$ and $Q_6$), and project equilibrium state points onto the ($t, Q_6$) plane, or order map. The order map evolves from water-like behavior to hard-sphere-like behavior upon varying $\lambda$ between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres ($\lambda=1$) and water-like ($\lambda\sim4/7$) with a family of tunable spherically-symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range $0\leq\lambda\leq1$, water-like structural anomalies (i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated $t$ and $Q_6$ in the anomalous region) occur only around $\lambda=4/7$. Water-like anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, orientation-dependent interactions being absent by design., Comment: total 21 pages, 6 figures

We use molecular dynamics simulations to probe the rotational dynamics of the SPC/E model of water for a range of temperatures down to 200 K, 13 K above to the mode coupling temperature. We find that rotational dynamics is spatially heterogeneous, i.e., there are clusters of molecules that rotate significantly more than the average for a given time interval, and we study the size and the temporal behavior of these clusters. We find that the position of a rotational heterogeneity is strongly correlated with the position of a translational heterogeneity, and that the fraction of molecules belonging to both kinds of heterogeneities increases with decreasing temperature. We further find that although the two types of heterogeneities are not identical, they are related to the same physical picture., Comment: 10 pages

We perform molecular dynamics simulations of 512 water-like molecules that interact via the TIP5P potential and are confined between two smooth hydrophobic plates that are separated by 1.10 nm. We find that the anomalous thermodynamic properties of water are shifted to lower temperatures relative to the bulk by $\approx 40$ K. The dynamics and structure of the confined water resemble bulk water at higher temperatures, consistent with the shift of thermodynamic anomalies to lower temperature. Due to this $T$ shift, our confined water simulations (down to $T = 220$ K) do not reach sufficiently low temperature to observe a liquid-liquid phase transition found for bulk water at $T\approx 215$ K using the TIP5P potential. We find that the different crystalline structures that can form for two different separations of the plates, 0.7 nm and 1.10 nm, have no counterparts in the bulk system, and discuss the relevance to experiments on confined water., Comment: 31 pages, 14 figures

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter $Q$ and translational order parameter $\tau$ increase. At T=0 K, the glasses fall on a line in the $Q$-$\tau$ plane or {\it order map}. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, $e_{IS}(T)$, and find that both order parameters for the IS are proportional to $e_{IS}$. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA)., Comment: submitted

We describe the phase diagram of amorphous solid water by performing molecular dynamics simulations. Our simulations follow different paths in the phase diagram: isothermal compression/decompression, isochoric cooling/heating and isobaric cooling/heating. We are able to identify low-density amorphous (LDA), high-density amorphous (HDA), and very-high density amorphous (VHDA) ices. The density $\rho$ of these glasses at different pressure $P$ and temperature $T$ agree well with experimental values. We also study the radial distribution functions of glassy water. We obtain VHDA by isobaric heating of HDA, as in experiment. We also find that ``other forms'' of glassy water can be obtained upon isobaric heating of LDA, as well as amorphous ices formed during the transformation of LDA to HDA. We argue that these other forms of amorphous ices, as well as VHDA, are not altogether new glasses but rather are the result of aging induced by heating. Samples of HDA and VHDA with different densities are recovered at normal $P$, showing that there is a continuum of glasses. Furthermore, the two ranges of densities of recovered HDA and recovered VHDA overlap at ambient $P$. Our simulations are consistent with the possibility of HDA$\to$LDA and VHDA$\to$LDA transformations, reproducing the experimental findings. We do not observe a VHDA$\to$HDA transformation.

It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous (LDA) ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second "distinct" high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations, and find that VHDA is a more stable form of HDA and that in fact VHDA should be considered as the amorphous ice of the quenched HDL., Comment: 5 pages, 4 figs

We report a molecular dynamics simulation study of the properties of the potential energy landscape sampled by a system of water molecules during the process of generating a glass by cooling, and during the process of regenerating the equilibrium liquid by heating the glass. We study the dependence of these processes on the cooling/heating rates as well as on the role of aging (the time elapsed in the glass state). We compare the properties of the potential energy landscape sampled during these processes with the corresponding properties sampled in the liquid equilibrium state to elucidate under which conditions glass configurations can be associated with equilibrium liquid configurations., Comment: to be published in Phys. Rev. E (rapid comunication)

We report a computer simulation study of the glass transition for water. To mimic the difference between standard and hyperquenched glass, we generate glassy configurations with different cooling rates and calculate the $T$ dependence of the specific heat on heating. The absence of crystallization phenomena allows us, for properly annealed samples, to detect in the specific heat the simultaneous presence of a weak pre-peak (``shadow transition''), and an intense glass transition peak at higher temperature. We discuss the implications for the currently debated value of the glass transition temperature of water. We also compare our simulation results with the Tool-Narayanaswamy-Moynihan phenomenological model., Comment: submitted to Phys. Rev

We study the potential energy landscape explored during a compression-decompression cycle for the SPC/E (extended simple point charge) model of water. During the cycle, the system changes from low density amorphous ice (LDA) to high density amorphous ice (HDA). After the cycle, the system does not return to the same region of the landscape, supporting the interesting possibility that more than one significantly different configuration corresponds to LDA. We find that the regions of the landscape explored during this transition have properties remarkably different from those explored in thermal equilibrium in the liquid phase.

We investigate the spatially heterogeneous dynamics in the SPC/E model of water by using molecular dynamics simulations. We relate the average mass $n^*$ of mobile particle clusters to the diffusion constant and the configurational entropy. Hence, $n^*$ can be interpreted as the mass of the ``cooperatively rearranging regions'' that form the basis of the Adam-Gibbs theory of the dynamics of supercooled liquids. Finally, we examine the time and temperature dependence of these transient clusters., Comment: 13 pages, 4 figs

The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories -- the set of local minima visited by the liquid -- offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely-studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS separated by relatively small energy barriers. We find that while the system \emph{travels} through these IS, the structure of the bond network continuously modifies, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216 molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ($\approx 1$ fs). Hence for water, the transitions between each of these IS is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes, the molecules with the greatest displacements move in small ``clusters'' of 1-10 molecules with displacements of $\approx 0.02-0.2$ nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear ``string-like'' clusters formed in a supercooled Lennar d-Jones system found by Glotzer and her collaborators., Comment: accepted in PRE