Communication: Re-entrant limits of stability of the liquid phase and the Speedy scenario in colloidal model systems

Thermodynamic anomalies, polyamorphism and all that

The appearance and evolution of thermodynamics anomalies, and related properties, are studied for two classes of system, modelling those dominated by covalent and ionic interactions, respectively. Such anomalies are most familiar in the density but are also present in other thermodynamics variables such as the compressibility and heat capacity. By systematically varying key model parameters the emergence and evolution of these anomalies can be tracked across the phase space. The interaction of the anomalies can often be rationalized by thermodynamics 'rules'. The emergence of these anomalies may also be correlated with the appearance of polyamorphism, the existence of multiple amorphous states which differ in density and entropy. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

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.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Thermodynamic anomalies in silicon and the relationship to the phase diagram

The evolution of thermodynamic anomalies are investigated in the pressure-temperature (pT) plane for silicon using the well-established Stillinger-Weber potential. Anomalies are observed in the density, compressibility and heat capacity. The relationships between them and with the liquid stability limit are investigated and related to the known thermodynamic constraints. The investigations are extended into the deeply supercooled regime using replica exchange techniques. Thermodynamic arguments are presented to justify the extension to low temperature, although a region of phase space is found to remain inaccessible due to unsuppressible crystallisation. The locus corresponding to the temperature of minimum compressibility is shown to display a characteristic 'S'-shape in thepTprojection which appears correlated with the underlying crystalline phase diagram. The progression of the anomalies is compared to the known underlying phase diagrams for both the crystal/liquid and amorphous/liquid states. The locations of the anomalies are also compared to those obtained from previous simulation work and (limited) experimental observations.

Anomalous Behavior in the Nucleation of Ice at Negative Pressures

Ice nucleation is a phenomenon that, despite the relevant implications for life, atmospheric sciences, and technological applications, is far from being completely understood, especially under extreme thermodynamic conditions. In this work we present a computational investigation of the homogeneous ice nucleation at negative pressures. By means of the seeding technique we estimate the size of the ice critical nucleus N_{c} for the TIP4P/Ice water model. This is done along the isotherms 230, 240, and 250 K, from positive to negative pressures until reaching the liquid-gas kinetic stability limit (where cavitation cannot be avoided). We find that N_{c} is nonmonotonic upon depressurization, reaching a minimum at negative pressures in the doubly metastable region of water. According to classical nucleation theory we establish the nucleation rate J and the surface tension γ, revealing a retracing behavior of both when the liquid-gas kinetic stability limit is approached. We also predict a reentrant behavior of the homogeneous nucleation line. The reentrance of these properties is related to the reentrance of the coexistence line at negative pressure, revealing new anomalies of water. The results of this work suggest the possibility of having metastable samples of liquid water for long times at negative pressure provided that heterogeneous nucleation is suppressed.

The progression of thermodynamic anomalies in MX2 networks with local tetrahedral geometries

Key thermodynamic anomalies in density and compressibility, as well as the related stability limits, are determined using an ionic model for BeF₂ which includes many-body polarization terms. BeF₂ is chosen as an example of an archetypal network-forming system whose structure can be rationalised in terms of connected local tetrahedral coordination polyhedra. The anion dipole polarizability (which effectively controls the bond angles linking neighbouring tetrahedra) is used as a single free parameter in order to help rationalise the changes in the anomaly locations in phase space, whilst all other potential parameters remain fixed. The anomalies and stability limits systematically shift to lower temperature and higher pressure as the anion polarizability is increased. At high dipole polarizabilities the temperature of maximum density anomaly locus becomes suppressed into the supercooled regime of the phase space. The movements of the anomaly loci are analysed in terms of the network structure and the correlation with the inter-tetrahedral bond angles is considered. The high sensitivity of the anomalies to the details of the potential models applied is discussed with reference to previous works on related systems. The relationship to analogous studies on Stillinger-Weber liquids is discussed.

Density anomaly of water at negative pressures from first principles

Using molecular dynamics simulations based on ab initio trained high-dimensional neural network potentials, we study the equation of state of liquid water at negative pressures. From density isobars computed for various pressures down to p  =  -230 MPa we determine the line of density maxima for two potentials based on the BLYP and the RPBE functionals, respectively. In both cases, dispersion corrections are included to account for non-local long-range correlations that give rise to van der Waals forces. We have followed the density maximum down to negative pressures close to the spinodal instability. For both functionals, the temperature of maximum density increases with decreasing pressure under moderate stretching, but changes slope at [Formula: see text] MPa and [Formula: see text] MPa for BLYP and RPBE, respectively. Our calculations confirm qualitatively the retracing shape of the line of density maxima found for empirical water models, indicating that the spinodal line maintains a positive slope even at strongly negative pressures.

Potential energy landscape of TIP4P/2005 water

We report a numerical study of the statistical properties of the potential energy landscape of TIP4P/2005, one of the most accurate rigid water models. We show that, in the region where equilibrated configurations can be generated, a Gaussian landscape description is able to properly describe the model properties. We also find that the volume dependence of the landscape properties is consistent with the existence of a locus of density maxima in the phase diagram. The landscape-based equation of state accurately reproduces the TIP4P/2005 pressure-vs-volume curves, providing a sound extrapolation of the free-energy at low T. A positive-pressure liquid-liquid critical point is predicted by the resulting free-energy.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Water-like anomalies as a function of tetrahedrality

Water is the most common and yet least understood material on Earth. Despite its simplicity, water tends to form tetrahedral order locally by directional hydrogen bonding. This structuring is known to be responsible for a vast array of unusual properties, e.g., the density maximum at 4 °C, which play a fundamental role in countless natural and technological processes, with the Earth’s climate being one of the most important examples. By systematically tuning the degree of tetrahedrality, we succeed in continuously interpolating between water-like behavior and simple liquid-like behavior. Our approach reveals what physical factors make water so anomalous and special even compared with other tetrahedral liquids.

Tetrahedral interactions describe the behavior of the most abundant and technologically important materials on Earth, such as water, silicon, carbon, germanium, and countless others. Despite their differences, these materials share unique common physical behaviors, such as liquid anomalies, open crystalline structures, and extremely poor glass-forming ability at ambient pressure. To reveal the physical origin of these anomalies and their link to the shape of the phase diagram, we systematically study the properties of the Stillinger–Weber potential as a function of the strength of the tetrahedral interaction λ. We uncover a unique transition to a reentrant spinodal line at low values of λ, accompanied with a change in the dynamical behavior, from non-Arrhenius to Arrhenius. We then show that a two-state model can provide a comprehensive understanding on how the thermodynamic and dynamic anomalies of this important class of materials depend on the strength of the tetrahedral interaction. Our work establishes a deep link between the shape of the phase diagram and the thermodynamic and dynamic properties through local structural ordering in liquids and hints at why water is so special among all substances.

Wide-ranging Absolute Viscosity Measurements of Sub- and Supercritical 1,1,1-trifluoroethane (R143a)

The viscosity of 1,1,1-trifluoroethane (R143a) was measured with a piezoelectrically actuated, torsionally vibrating quartz sensor. The measurements extended over a temperature range from 300 K to 440 K with pressures to 68 MPa and covered states from the dilute gas to the compressed liquid. The influence of the drive voltage on the torsional displacement of the vibrator in fluid and in vacuum was systematically investigated. Since R143a is highly polar, the sample conductance and susceptance were also monitored with the sensor to detect possible electroviscous contributions in the measured viscosities. None were identified so that the estimated uncertainty of the measurements remains at 2 % at a 95 % confidence level (coverage factor k = 2). The results agree well within this margin with literature data that were determined with four other viscometric techniques.

Supercooled and glassy water: Metastable liquid(s), amorphous solid(s), and a no-man's land

We review the recent research on supercooled and glassy water, focusing on the possible origins of its complex behavior. We stress the central role played by the strong directionality of the water-water interaction and by the competition between local energy, local entropy, and local density. In this context we discuss the phenomenon of polyamorphism (i.e., the existence of more than one disordered solid state), emphasizing both the role of the preparation protocols and the transformation between the different disordered ices. Finally, we present the ongoing debate on the possibility of linking polyamorphism with a liquid-liquid transition that could take place in the no-man's land, the temperature-pressure window in which homogeneous nucleation prevents the investigation of water in its metastable liquid form.

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.

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids

In this paper, we develop a thermodynamic perturbation theory to describe the self-assembly of patchy colloids which exhibit both patch-patch attractions as well as patch/non-patch attractions. That is, patches attract other patches as well as the no patch region (we call this region Ψ). In general, the patch-patch and patch-Ψ attractions operate on different energy scales allowing for a competition between different modes of attraction. This competition may result in anomalous thermodynamic properties. As an application, we tune the patch parameters to reproduce the liquid density (suitably scaled) maximum of water. It is then shown that the liquid branch of the colloids phase diagram has liquid densities consistent with both saturated and super-cooled liquid water. Finally, it is shown that the colloids reproduce water's anomalous minimum in isothermal compressibility and negative volume expansivity.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).