Microscopic pathways of transition from low-density to high-density amorphous phase of water.

In recent years, much attention has been devoted to understanding the pathways of phase transition between two equilibrium condensed phases (such as liquids and solids). However, the microscopic pathways of transition involving non-equilibrium, non-diffusive amorphous (glassy) phases still remain poorly understood. In this work, we have employed computer simulations, persistence homology (a tool rooted in topological data analysis), and machine learning to probe the microscopic pathway of pressure-induced non-equilibrium transition between the low- and high-density amorphous (LDA and HDA, respectively) ice phases of the TIP4P/2005 and ST2 water models. Using persistence homology and machine learning, we introduced a new order parameter that unambiguously identifies the LDA- and HDA-like local environments. The LDA phase transitions continuously and collectively into the corresponding HDA phase via a pre-ordered intermediate phase during the isothermal compression. The local order parameter susceptibilities show a maximum near the transition pressure (P*)-suggesting maximum structural heterogeneities near P*. The HDA-like clusters are structurally ramified and spatially delocalized inside the LDA phase near the transition pressure. We also found manifestations of the first-order low-density to high-density liquid transition in the sharpness of the order parameter change during the LDA to HDA transition. We further investigated the (geometrical) structures and topologies of the LDA and HDA ices formed via different protocols and also studied the dependence of the (microscopic) pathway of phase transition on the protocol followed to prepare the initial LDA phase. Finally, the method adopted here to study the phase transition pathways is not restricted to the system under consideration and provides a robust way of probing phase transition pathways involving any two condensed phases at both equilibrium and out-of-equilibrium conditions.

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.

Thermodynamic analysis of the stability of planar interfaces between coexisting phases and its application to supercooled water.

Two-phase simulations are commonly used to evaluate coexistence conditions, interfacial tensions, and other thermodynamic properties associated with first-order phase transitions. Calculation of these properties is often simplified when the interfaces between the two phases are flat or planar. Here, we derive a general thermodynamic criterion for selecting simulation cell dimensions to stabilize planar interfaces in phase-separated fluid-fluid systems with respect to homogeneous, single-phase states. The resulting expression is validated by analyzing the effects of simulation cell dimensions on the formation of planar liquid-vapor interfaces in the Lennard-Jones fluid and in the TIP4P/2005 model of water. We also perform large scale molecular dynamics simulations to study metastable liquid-liquid phase separation in the ST2 and TIP4P/2005 models of water under deeply supercooled conditions. Our simulations confirm the stability of a liquid-liquid interface in ST2, and they demonstrate that the corresponding interface for TIP4P/2005 can be stabilized by judiciously choosing the simulation cell aspect ratio in a manner consistent with the thermodynamic criterion. We posit that this sensitivity to the simulation cell aspect ratio may explain discrepancies between previous studies examining liquid-liquid separation in models of supercooled water.

Thermodynamic Anomalies in Stretched Water.

Via molecular dynamics simulations of the TIP4P/2005 water model, we study liquid water's anomalous behavior at large negative pressure produced through isochoric cooling. We find that isochores without a pressure minimum can display "reentrant" behavior whereby a system that cavitates upon cooling can then rehomogenize upon further cooling. This behavior is a consequence of the underlying density maximum along the spinodal, but its actual manifestation in simulations is strongly influenced by finite size effects. These observations suggest that water under strong hydrophilic confinement may display richer phase behavior than hitherto assumed. This also suggests that propensity toward cavitation does not always correlate with greater tension, contrary to the prevailing assumption for interpreting water stretching experiments. We also show that a maximum spinodal density in water results in a locus of maximum compressibility and a minimum speed of sound that are independent from any influence of a liquid-liquid critical point (LLCP). However, we demonstrate that structural signatures of a Widom line, which likely emanates from an LLCP at elevated pressure, extend to large negative pressure, but such signatures are only observed upon sampling water's underlying potential energy landscape, rather than the thermalized metastable liquid.

Molecular modeling and structural characterization of a high glycine-tyrosine hair keratin associated protein.

High glycine-tyrosine (HGT) proteins are an important constituent of the keratin associated proteins (KAPs) present in human hair. The glassy state physics of hair fibres are thought to be largely regulated by KAPs, which exist in an amorphous state and are readily affected by environmental conditions. However, there are no studies characterizing the individual KAPs. In this paper, we present the first step to fill this gap by computational modeling and experimental studies on a HGT protein, KAP8.1. In particular, we have modeled the three-dimensional structure of this 63-residue protein using homology information from an anti-freeze protein in snow flea. The model for KAP8.1 is characterized by four strands of poly-proline II (or PPII) type helical secondary structures, held together by two cysteine disulphide bridges. Computer simulations confirm the stability of the modelled structure and show that the protein largely samples the PPII and ß-sheet conformations during the molecular dynamics simulations. Spectroscopic studies including Raman, IR and vibrational circular dichroism have also been performed on synthesized KAP8.1. The experimental studies suggest that KAP8.1 is characterised by ß-sheet and PPII structures, largely consistent with the simulation studies. The model built in this work is a good starting point for further simulations to study in greater depth the glassy state physics of hair, including its water sorption isotherms, glass transition, and the effect of HGT proteins on KAP matrix plasticization. These results are a significant step towards our goal of understanding how the properties of hair can be affected and manipulated under different environmental conditions of temperature, humidity, ageing and small molecule additives.

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions.

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal," the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.

Two-state thermodynamics and the possibility of a liquid-liquid phase transition in supercooled TIP4P/2005 water.

Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of different water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT, we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures ("states"). The results suggest the presence of a liquid-liquid critical point and are consistent with the existence of a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely, mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure.

Orientational order as the origin of the long-range hydrophobic effect.

The long range attractive force between two hydrophobic surfaces immersed in water is observed to decrease exponentially with their separation-this distance-dependence of effective force is known as the hydrophobic force law (HFL). We explore the microscopic origin of HFL by studying distance-dependent attraction between two parallel rods immersed in 2D Mercedes Benz model of water. This model is found to exhibit a well-defined HFL. Although the phenomenon is conventionally explained by density-dependent theories, we identify orientation, rather than density, as the relevant order parameter. The range of density variation is noticeably shorter than that of orientational heterogeneity. The latter is comparable to the observed distances of hydrophobic force. At large separation, attraction between the rods arises primarily from a destructive interference among the inwardly propagating oppositely oriented heterogeneity generated in water by the two rods. As the rods are brought closer, the interference increases leading to a decrease in heterogeneity and concomitant decrease in free energy of the system, giving rise to the effective attraction. We notice formation of hexagonal ice-like structures at the onset of attractive region which suggests that metastable free energy minimum may play a role in the origin of HFL.

Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water.

The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.

Solid-solid collapse transition in a two dimensional model molecular system.

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains.

Anisotropy induced crossover from weakly to strongly first order melting of two dimensional solids.

Melting and freezing transitions in two dimensional (2D) systems are known to show highly unusual characteristics. Most of the earlier studies considered atomic systems: the melting of 2D molecular solids is still largely unexplored. In order to understand the role of anisotropy as well as multiple energy and length scales present in molecular systems, here we report computer simulation studies of melting of 2D molecular systems. We computed a limited portion of the solid-liquid phase diagram. We find that the interplay between the strength of isotropic and anisotropic interactions can give rise to rich phase diagram consisting of isotropic liquid and two crystalline phases-honeycomb and oblique. The nature of the transition depends on the relative strength of the anisotropic interaction and a strongly first order melting turns into a weakly first order transition on increasing the strength of the isotropic interaction. This crossover can be attributed to an increase in stiffness of the solid phase free energy minimum on increasing the strength of the anisotropic interaction. The defects involved in melting of molecular systems are quite different from those known for the atomic systems.

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study.

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier (TΔΩv/min*) does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the TΔΩv/min* and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Sensitivity of nucleation phenomena on range of interaction potential.

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.

Microscopic Origin of Hysteresis in Water Sorption on Protein Matrices.

Despite the importance of water sorption isotherms for a fundamental understanding of protein-water interactions, the microscopic origin of hysteresis between the adsorption and desorption branches is not well understood. Using our recently developed simulation technique, we compute the water sorption isotherms of two proteins, lysozyme and Trp-cage, a miniprotein. We explicitly compare protein-water interactions in adsorption and desorption processes, by analyzing local hydration in terms of hydrogen bonding, water density, and solvent-accessible surface area. We find that significant differences in hydration behavior between adsorption and desorption manifest themselves at the individual amino acid level, in particular around polar or charged residues. We confirm this observation by demonstrating that Trp-cage's hysteresis can be significantly reduced by mutating charged residues to alanine, a neutral and nonpolar amino acid.

Effects of disulfide bridges and backbone connectivity on water sorption by protein matrices.

Understanding the water sorption behavior of protein powders is important in applications such as the preservation of protein-based pharmaceuticals. Most globular proteins exhibit a characteristic sigmoidal water adsorption isotherm at ambient conditions. However, it is not well understood how water sorption behavior is influenced by intrinsic factors that are related to structural properties of proteins. We investigate computationally how structural constraints on proteins influence the water sorption isotherms of amorphous protein powders. Specifically, we study the effects of non-local disulfide linkages and backbone connectivity using pheromone ER-23 and lysozyme as model proteins. We find that non-local disulfide linkages can significantly restrict structural changes during hydration and dehydration, and this in turn greatly reduces the extent of hysteresis between the adsorption and desorption branches. Upon removing the backbone connectivity by breaking all peptide bonds in lysozyme, we find that the hysteresis shifts towards the lower humidity regime, and the water uptake capacity is significantly enhanced. We attribute these changes to the higher aggregation propensity of the constraint-free amino acids in dehydrated condition, and the formation of a spanning water network at high hydration levels.

Nucleation of a stable solid from melt in the presence of multiple metastable intermediate phases: wetting, Ostwald's step rule, and vanishing polymorphs.

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. Sometimes, the metastable phase might have a lower free energy minimum than the liquid but higher than the stable-solid-phase minimum and have characteristics in between the parent liquid and the globally stable solid phase. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier because surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work, we discuss a density functional theory (DFT)-based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order-parameter-dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier, and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of the Ostwald step rule and the well-known phenomenon of "disappearing polymorphs" that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics, some of which may be explored via modern nanoscopic synthetic methods.