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).

A continuum of amorphous ices between low-density and high-density amorphous ice.

Amorphous ices are usually classified as belonging to low-density or high-density amorphous ice (LDA and HDA) with densities ρLDA ≈ 0.94 g/cm3 and ρHDA ≈ 1.15-1.17 g/cm3. However, a recent experiment crushing hexagonal ice (ball-milling) produced a medium-density amorphous ice (MDA, ρMDA ≈ 1.06 g/cm3) adding complexity to our understanding of amorphous ice and the phase diagram of supercooled water. Motivated by the discovery of MDA, we perform computer simulations where amorphous ices are produced by isobaric cooling and isothermal compression/decompression. Our results show that, depending on the pressure employed, isobaric cooling can generate a continuum of amorphous ices with densities that expand in between those of LDA and HDA (briefly, intermediate amorphous ices, IA). In particular, the IA generated at P ≈ 125 MPa has a remarkably similar density and average structure as MDA, implying that MDA is not unique. Using the potential energy landscape formalism, we provide an intuitive qualitative understanding of the nature of LDA, HDA, and the IA generated at different pressures. In this view, LDA and HDA occupy specific and well-separated regions of the PEL; the IA prepared at P = 125 MPa is located in the intermediate region of the PEL that separates LDA and HDA.

The Harmonic and Gaussian Approximations in the Potential Energy Landscape Formalism for Quantum Liquids.

The potential energy landscape (PEL) formalism has been used in the past to describe the behavior of classical low-temperature liquids and glasses. Here, we extend the PEL formalism to describe the behavior of liquids and glasses that obey quantum mechanics. In particular, we focus on the (i) harmonic and (ii) Gaussian approximations of the PEL, which have been commonly used to describe classical systems, and show how these approximations can be applied to quantum liquids/glasses. Contrary to the case of classical liquids/glasses, the PEL of quantum liquids is temperature-dependent, and hence, the main expressions resulting from approximations (i) and (ii) depend on the nature (classical vs quantum) of the system. The resulting theoretical expressions from the PEL formalism are compared with results from path-integral Monte Carlo (PIMC) simulations of a monatomic model liquid. In the PIMC simulations, every atom of the quantum liquid is represented by a ring-polymer. Our PIMC simulations show that at the local minima of the PEL (inherent structures, or IS), sampled over a wide range of temperatures and volumes, the ring-polymers are collapsed. This considerably facilitates the description of quantum liquids using the PEL formalism. Specifically, the normal modes of the ring-polymer system/quantum liquid at an IS can be calculated analytically if the normal modes of the classical liquid counterpart are known (as obtained, e.g., from classical MC or molecular dynamics simulations of the corresponding atomic liquid).

Harvesting Energy from Changes in Relative Humidity Using Nanoscale Water Capillary Bridges.

We show that nanoscale water capillary bridges (WCB) formed between patchy surfaces can extract energy from the environment when subjected to changes in relative humidity (RH). Our results are based on molecular dynamics simulations combined with a modified version of the Laplace-Kelvin equation, which is validated using the nanoscale WCB. The calculated energy density harvested by the nanoscale WCB is relevant, ≈1700 kJ/m3, and is comparable to the energy densities harvested using available water-responsive materials that expand and contract due to changes in RH.

The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice.

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (Ih) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice Ih. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice Ih increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice Ih. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient αP(T) and bulk modulus B(T) of both LDA and ice Ih. Remarkably, the ρ(T), αP(T), and B(T) of LDA are practically identical to those of ice Ih. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice Ih. H atoms delocalize considerably (over a distance ≈ 20-25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

Liquid-liquid phase separation in supercooled water from ultrafast heating of low-density amorphous ice.

Recent experiments continue to find evidence for a liquid-liquid phase transition (LLPT) in supercooled water, which would unify our understanding of the anomalous properties of liquid water and amorphous ice. These experiments are challenging because the proposed LLPT occurs under extreme metastable conditions where the liquid freezes to a crystal on a very short time scale. Here, we analyze models for the LLPT to show that coexistence of distinct high-density and low-density liquid phases may be observed by subjecting low-density amorphous (LDA) ice to ultrafast heating. We then describe experiments in which we heat LDA ice to near the predicted critical point of the LLPT by an ultrafast infrared laser pulse, following which we measure the structure factor using femtosecond x-ray laser pulses. Consistent with our predictions, we observe a LLPT occurring on a time scale < 100 ns and widely separated from ice formation, which begins at times >1 µs.

Anomalous properties in the potential energy landscape of a monatomic liquid across the liquid-gas and liquid-liquid phase transitions.

As a liquid approaches the gas state, the properties of the potential energy landscape (PEL) sampled by the system become anomalous. Specifically, (i) the mechanically stable local minima of the PEL [inherent structures (IS)] can exhibit cavitation above the so-called Sastry volume, vS, before the liquid enters the gas phase. In addition, (ii) the pressure of the liquid at the sampled IS [i.e., the PEL equation of state, PIS(v)] develops a spinodal-like minimum at vS. We perform molecular dynamics simulations of a monatomic water-like liquid and verify that points (i) and (ii) hold at high temperatures. However, at low temperatures, cavitation in the liquid and the corresponding IS occurs simultaneously and a Sastry volume cannot be defined. Remarkably, at intermediate/high temperatures, the IS of the liquid can exhibit crystallization, i.e., the liquid regularly visits the regions of the PEL that belong to the crystal state. The model liquid considered also exhibits a liquid-liquid phase transition (LLPT) between a low-density and a high-density liquid (LDL and HDL). By studying the behavior of PIS(v) during the LLPT, we identify a Sastry volume for both LDL and HDL. The HDL Sastry volume marks the onset above which IS are heterogeneous (composed of LDL and HDL particles), analogous to points (i) and (ii) above. However, the relationship between the LDL Sastry volume and the onset of heterogeneous IS is less evident. We conclude by presenting a thermodynamic argument that can explain the behavior of the PEL equation of state PIS(v) across both the liquid-gas phase transition and LLPT.

Different temperature- and pressure-effects on the water-mediated interactions between hydrophobic, hydrophilic, and hydrophobic-hydrophilic nanoscale surfaces.

Water-mediated interactions (WMIs) are responsible for diverse processes in aqueous solutions, including protein folding and nanoparticle aggregation. WMI may be affected by changes in temperature and pressure, and hence, they can alter chemical/physical processes that occur in aqueous environments. Traditionally, attention has been focused on hydrophobic interactions while, in comparison, the role of hydrophilic and hybrid (hydrophobic-hydrophilic) interactions have been mostly overlooked. Here, we study the role of T and P on the WMI between nanoscale (i) hydrophobic-hydrophobic, (ii) hydrophilic-hydrophilic, and (iii) hydrophilic-hydrophobic pairs of (hydroxylated/non-hydroxylated) graphene-based surfaces. We find that hydrophobic, hydrophilic, and hybrid interactions are all sensitive to P. However, while hydrophobic interactions [case (i)] are considerably sensitive to T-variations, hydrophilic [case (ii)] and hybrid interactions [case (iii)] are practically T-independent. An analysis of the entropic and enthalpic contributions to the potential of mean force for cases (i)-(iii) is also presented. Our results are important in understanding T- and P-induced protein denaturation and the interactions of biomolecules in solution, including protein aggregation and phase separation processes. From the computational point of view, the results presented here are relevant in the design of implicit water models for the study of molecular and colloidal/nanoparticle systems at different thermodynamic conditions.

Nuclear quantum effects on the dynamics and glass behavior of a monatomic liquid with two liquid states.

We perform path integral molecular dynamics (PIMD) simulations of a monatomic liquid that exhibits a liquid-liquid phase transition and liquid-liquid critical point. PIMD simulations are performed using different values of Planck's constant h, allowing us to study the behavior of the liquid as nuclear quantum effects (NQE, i.e., atoms delocalization) are introduced, from the classical liquid (h = 0) to increasingly quantum liquids (h > 0). By combining the PIMD simulations with the ring-polymer molecular dynamics method, we also explore the dynamics of the classical and quantum liquids. We find that (i) the glass transition temperature of the low-density liquid (LDL) is anomalous, i.e., Tg LDL(P) decreases upon compression. Instead, (ii) the glass transition temperature of the high-density liquid (HDL) is normal, i.e., Tg HDL(P) increases upon compression. (iii) NQE shift both Tg LDL(P) and Tg HDL(P) toward lower temperatures, but NQE are more pronounced on HDL. We also study the glass behavior of the ring-polymer systems associated with the quantum liquids studied (via the path-integral formulation of statistical mechanics). There are two glass states in all the systems studied, low-density amorphous ice (LDA) and high-density amorphous ice (HDA), which are the glass counterparts of LDL and HDL. In all cases, the pressure-induced LDA-HDA transformation is sharp, reminiscent of a first-order phase transition. In the low-quantum regime, the LDA-HDA transformation is reversible, with identical LDA forms before compression and after decompression. However, in the high-quantum regime, the atoms become more delocalized in the final LDA than in the initial LDA, raising questions on the reversibility of the LDA-HDA transformation.

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.

The role of high-density and low-density amorphous ice on biomolecules at cryogenic temperatures: a case study with polyalanine.

Experimental techniques, such as cryo-electron microscopy, require biological samples to be recovered at cryogenic temperatures (T ≈ 100 K) with water being in an amorphous ice state. However, (bulk) water can exist in two amorphous ices at P < 1 GPa, low-density amorphous (LDA) ice at low pressures and high-density amorphous ice (HDA) at high pressures; HDA is ≈20-25% denser than LDA. While fast/plunge cooling at 1 bar brings the sample into LDA, high-pressure cooling (HPC), at sufficiently high pressure, produces HDA. HDA can also be produced by isothermal compression of LDA at cryogenic temperatures. Here, we perform classical molecular dynamics simulations to study the effects of LDA, HDA, and the LDA-HDA transformation on the structure and hydration of a small peptide, polyalanine. We follow thermodynamic paths corresponding to (i) fast/plunge cooling at 1 bar, (ii) HPC at P = 400 MPa, and (iii) compression/decompression cycles at T = 80 K. While process (i) produced LDA in the system, path (iii) produces HDA. Interestingly, the amorphous ice produced in process (ii) is an intermediate amorphous ice (IA) with properties that fall in-between those of LDA and HDA. Remarkably, the structural changes in polyalanine are negligible at all conditions studied (0-2000 MPa, 80-300 K) even when water changes among the low and high-density liquid states as well as the amorphous solids LDA, IA, and HDA. The similarities and differences in the hydration of polyalanine vitrified in LDA, IA, and HDA are described. Since the studied thermodynamic paths are suitable for the cryopreservation of biomolecules, we also study the structure and hydration of polyalanine along isobaric and isochoric heating paths, which can be followed experimentally for the recovery of cryopreserved samples. Upon heating, the structure of polyalanine remains practically unchanged. We conclude with a brief discussion of the practical advantages of (a) using HDA and IA as a cryoprotectant environment (as opposed to LDA), and (b) the use of isochoric heating as a recovery process (as opposed to isobaric heating).

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 αP(T), isothermal compressibility κT(T), isobaric heat capacity CP(T), and static dielectric constant ε(T). While these properties are in excellent [αP(T) and κT(T)] or semi-quantitative agreement [CP(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 CP(T) and κT(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κT(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in CP(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 CP(T), D(T), and structural properties being the only (expected) exceptions.

Experimental observation of the liquid-liquid transition in bulk supercooled water under pressure.

We prepared bulk samples of supercooled liquid water under pressure by isochoric heating of high-density amorphous ice to temperatures of 205 ± 10 kelvin, using an infrared femtosecond laser. Because the sample density is preserved during the ultrafast heating, we could estimate an initial internal pressure of 2.5 to 3.5 kilobar in the high-density liquid phase. After heating, the sample expanded rapidly, and we captured the resulting decompression process with femtosecond x-ray laser pulses at different pump-probe delay times. A discontinuous structural change occurred in which low-density liquid domains appeared and grew on time scales between 20 nanoseconds to 3 microseconds, whereas crystallization occurs on time scales of 3 to 50 microseconds. The dynamics of the two processes being separated by more than one order of magnitude provides support for a liquid-liquid transition in bulk supercooled water.

Energy Stored in Nanoscale Water Capillary Bridges between Patchy Surfaces.

We perform molecular dynamics (MD) simulations of a water capillary bridge (WCB) expanding between two identical chemically heterogeneous surfaces. The model surfaces, based on the structure of silica, are hydrophobic and are decorated by a hydrophilic (hydroxylated silica) patch that is in contact with the WCB. Our MD simulations results, including the WCB profile and forces induced on the walls, are in agreement with capillarity theory even at the smallest wall separations studied, h = 2.5-3 nm. Remarkably, the energy stored in the WCB can be relatively large, with an energy density that is comparable to that harvested by water-responsive materials used in actuators and nanogenerators.

Comparative Study of Water-Mediated Interactions between Hydrophilic and Hydrophobic Nanoscale Surfaces.

Self-assembly processes in aqueous solutions, such as protein folding and nanoparticle aggregation, are driven by water-mediated interactions (WMIs). The most common of such interactions are the attractive forces between hydrophobic units. While numerous studies have focused on hydrophobic interactions, WMIs between hydrophilic moieties and pairs of hydrophilic-hydrophobic surfaces have received much less attention. In this work, we perform molecular dynamics simulations to study the WMI between nanoscale (i) hydrophobic-hydrophobic, (ii) hydrophilic-hydrophilic, and (iii) hydrophilic-hydrophobic pairs of (hydroxylated/nonhydroxylated) graphene-based surfaces. We find that in all cases, the potential of mean force (PMF) between the plates exhibits oscillations as a function of the plate separations r, up to r ≈ 1-1.5 nm. The local minima of the PMF, which define the stable/metastable states of the system, correspond to plates' separations at which water molecules arrange into n = 0, 1, 2, ... layers between the plates. In case (i), the stable state of the system corresponds to the plates in contact with one another. Instead, in cases (ii) and (iii), water is never removed between the plates. The free-energy barriers separating the stable/metastable states of the system vary with the hydrophilicity/hydrophobicity of the interacting plates. However, the effective forces between the plates are comparable in magnitude. This strongly suggests that hydrophilic-hydrophilic and hydrophilic-hydrophobic interactions can play a relevant role in self-assembly processes in aqueous solutions, alike hydrophobic interactions. Interestingly, we find that the WMIs between hydrophilic-hydrophilic and hydrophilic-hydrophobic plates are similar, suggesting that only one hydrophilic surface is sufficient to induce hydrophilic-like WMI. We also briefly discuss the role of surface polarity on the WMI. In particular, we show that depending on the surface polarity, WMI can exhibit mixed features characteristic of hydrophobic and hydrophilic interactions. Our results suggest that the forces between hydrophobic, hydrophilic, and hydrophobic/hydrophilic surfaces are all relevant in driving a self-assembly system toward its final state, but it is the hydrophobic interaction that provides stability to such a final state.

Glass polymorphism and liquid-liquid phase transition in aqueous solutions: experiments and computer simulations.

One of the most intriguing anomalies of water is its ability to exist as distinct amorphous ice forms (glass polymorphism or polyamorphism). This resonates well with the possible first-order liquid-liquid phase transition (LLPT) in the supercooled state, where ice is the stable phase. In this Perspective, we review experiments and computer simulations that search for LLPT and polyamorphism in aqueous solutions containing salts and alcohols. Most studies on ionic solutes are devoted to NaCl and LiCl; studies on alcohols have mainly focused on glycerol. Less attention has been paid to protein solutions and hydrophobic solutes, even though they reveal promising avenues. While all solutions show polyamorphism and an LLPT only in dilute, sub-eutectic mixtures, there are differences regarding the nature of the transition. Isocompositional transitions for varying mole fractions are observed in alcohol but not in ionic solutions. This is because water can surround alcohol molecules either in a low- or high-density configuration whereas for ionic solutes, the water ion hydration shell is forced into high-density structures. Consequently, the polyamorphic transition and the LLPT are prevented near the ions, but take place in patches of water within the solutions. We highlight discrepancies and different interpretations within the experimental community as well as the key challenges that need consideration when comparing experiments and simulations. We point out where reinterpretation of past studies helps to draw a unified, consistent picture. In addition to the literature review, we provide original experimental results. A list of eleven open questions that need further consideration is identified.

Glass polymorphism in TIP4P/2005 water: A description based on the potential energy landscape formalism.

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, eIS(V), is a concave function of the volume and (ii) the IS pressure, PIS(V), exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a nonmonotonic 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 with LDA and another with 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.

State variables for glasses: The case of amorphous ice.

Glasses are out-of-equilibrium systems whose state cannot be uniquely defined by the usual set of equilibrium state variables. Here, we seek to identify an expanded set of variables that uniquely define the state of a glass. The potential energy landscape (PEL) formalism is a useful approach within statistical mechanics to describe supercooled liquids and glasses. We use the PEL formalism and computer simulations to study the transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA). We employ the ST2 water model, which exhibits an abrupt first-order-like phase transition from LDA to HDA, similar to that observed in experiments. We prepare a number of distinct samples of both LDA and HDA that have completely different preparation histories. We then study the evolution of these LDA and HDA samples during compression and decompression at temperatures sufficiently low that annealing is absent and also during heating. We find that the evolution of each glass sample, during compression/decompression or heating, is uniquely determined by six macroscopic properties of the initial glass sample. These six quantities consist of three conventional thermodynamic state variables, the number of molecules N, the system volume V, and the temperature T, as well as three properties of the PEL, the inherent structure (IS) energy EIS, the IS pressure PIS, and the average curvature of the PEL at the IS SIS. In other words, (N,V,T,EIS,PIS,SIS) are state variables that define the glass state in the case of amorphous ice. An interpretation of our results in terms of the PEL formalism is provided. Since the behavior of water in the glassy state is more complex than for most substances, our results suggest that these six state variables may be applicable to amorphous solids in general and that there may be situations in which fewer than six variables would be sufficient to define the state of a glass.

Comparative Study of the Effects of Temperature and Pressure on the Water-Mediated Interactions between Apolar Nanoscale Solutes.

We perform molecular dynamics simulations to study the effects of temperature and pressure on the water-mediated interaction (WMI) between two nanoscale (apolar) graphene plates at 240 ≤ T ≤ 400 K and -100 ≤ P ≤ 1200 MPa. These are thermodynamic conditions relevant to, for example, cooling-, heating-, compression-, and decompression-induced protein denaturation. We find that at all ( T, P) studied, the potential of mean force between the graphene plates, as a function of plate separation r, exhibits local minima at specific plate separations r = r n that can accommodate n water layers ( n = 0,1,2,3). In particular, our results show that isobaric cooling and isothermal compression have a similar effect on WMI between the plates; both processes tend to suppress the attraction and ultimate collapse of the graphene plates by kinetically trapping the plates at the metastable states with r = r n ( n > 0). In addition, isobaric heating and isothermal decompression also have a similar effect; both processes tend to reduce the range and strength of the interactions between the graphene plates. Interestingly, at low temperatures, the WMI between the plates is affected by crystallization. However, crystallization depends deeply on the water model considered, SPC/E and TIP4P/2005 water models, with the crystallization occurring at different ( T, P) conditions, into different forms of ice.

Temperature Effects on Water-Mediated Interactions at the Nanoscale.

We perform molecular dynamics simulations to study the effects of temperature on the water-mediated interactions between nanoscale apolar solutes. Specifically, we calculate the potential of mean force (PMF) between two graphene plates immersed in water at 240 ≤ T ≤ 400 K and P = 0.1 MPa. These are thermodynamic conditions relevant to cooling- and heating-induced protein denaturation. It is found that both cooling and heating tend to suppress the attraction, and ultimate collapse, of the graphene plates. However, the underlying role played by water upon heating and cooling is different. Isobaric heating reduces the strength and range of the interactions between the plates. Instead, isobaric cooling stabilizes the plates separations that can accommodate an integer number of water layers between the graphene plates. In particular, the energy barriers separating these plate separations increase linearly with 1/ T. We also explore the sensitivity of the plates PMF to the water model employed. In the case of the TIP4P/2005 model, water confined between the plates crystallizes into a defective bilayer ice at low temperatures, whereas in the case of the SPC/E model, water remains in the liquid state at same thermodynamic conditions. The effects of varying water-graphene interactions on the plates PMF are also studied.