John Russo

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Understanding water’s anomalies with locally favoured structures

Water is a complex liquid that displays a surprising array of unusual properties, the most famous being the density maximum at about 4 °C. The origin of these anomalies is still a matter of debate, and so far a quantitative description of waters phase behaviour starting from the molecular arrangements is still missing. Here we report a study of the microscopic structural features of water as obtained from computer simulations. We identify locally favoured structures having a high degree of translational order in the second shell, and a two-state model is used to describe the behaviour of liquid water over a wide region of the phase diagram. Furthermore, we show that locally favoured structures not only have translational order in the second shell but also contain five-membered rings of hydrogen-bonded molecules. This suggests their mixed character: the former helps crystallization, whereas the latter causes frustration against crystallization.

Crystal nucleation as the ordering of multiple order parameters

Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition, the process occurs between phases of different symmetry, and it is thus inherently a multi-dimensional process, in which all symmetries are broken at the transition. In this Focus Article, we consider some recent studies which highlight the multi-dimensional nature of the nucleation process. Even for a single-component system, the formation of solid crystals from the metastable melt involves fluctuations of two (or more) order parameters, often associated with the decoupling of positional and orientational symmetry breaking. In other words, we need at least two order parameters to describe the free-energy of a system including its liquid and crystalline states. This decoupling occurs naturally for asymmetric particles or directional interactions, focusing here on the case of water, but we will show that it also affects spherically symmetric interacting particles, such as the hard-sphere system. We will show how the treatment of nucleation as a multi-dimensional process has shed new light on the process of polymorph selection, on the effect of external fields on the nucleation process and on glass-forming ability.

Assessing the role of static length scales behind glassy dynamics in polydisperse hard disks

Significance The origin of dynamical slowing down toward glass transition is a fundamental unsolved problem in condensed matter physics. A crucial question is whether this slowing down has a structural origin. Recently, a method to detect hidden order within the fluid was proposed, based on the idea that freezing a fraction of the particles in a system causes a transition akin to glass transition. Here, we show that a glass former, polydisperse hard disks, has a strong increase of structural order, well correlated with slow dynamics, which goes undetected by the pinning method. This casts doubt on the order-agnostic qualities of the pinning length scale and keeps static length scales in the race for plausible explanations of the glass transition problem. The possible role of growing static order in the dynamical slowing down toward the glass transition has recently attracted considerable attention. On the basis of random first-order transition theory, a new method to measure the static correlation length of amorphous order, called “point-to-set” (PTS) length, has been proposed and used to show that the dynamic length grows much faster than the static length. Here, we study the nature of the PTS length, using a polydisperse hard-disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order and dynamic heterogeneity, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order-agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard-disk system is a typical glass former.

Nonclassical pathways of crystallization in colloidal systems

Colloidal systems offer ideal conditions to study the nucleation process, both from an experimental viewpoint, due to their relatively large size and long time scales, and from a modeling point of view, due to the tunability of their interactions. In this article, we review recent studies on the process of colloidal crystallization from a microscopic perspective. In particular, we focus on nonclassical pathways to nucleation, where the appearance of solid crystals involves fluctuations of two or more order parameters. Nonclassical behavior is interpreted as a decoupling of positional and orientational symmetry breaking. We then consider how the nucleation pathway determines which polymorph is selected upon nucleation from the melt. The study of nucleation pathways not only sheds new light on the microscopic mechanism of nucleation, but also provides important information regarding its avoidance, suggesting a deep link between crystallization and vitrification.

Common mechanism of thermodynamic and mechanical origin for ageing and crystallization of glasses

The glassy state is known to undergo slow structural relaxation, where the system progressively explores lower free-energy minima which are either amorphous (ageing) or crystalline (devitrification). Recently, there is growing interest in the unusual intermittent collective displacements of a large number of particles known as ‘avalanches’. However, their structural origin and dynamics are yet to be fully addressed. Here, we study hard-sphere glasses which either crystallize or age depending on the degree of size polydispersity, and show that a small number of particles are thermodynamically driven to rearrange in regions of low density and bond orientational order. This causes a transient loss of mechanical equilibrium which facilitates a large cascade of motion. Combined with previously identified phenomenology, we have a complete kinetic pathway for structural change which is common to both ageing and crystallization. Furthermore, this suggests that transient force balance is what distinguishes glasses from supercooled liquids.

Formation of porous crystals via viscoelastic phase separation

Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization follows three different routes: direct crystallization of the liquid phase, the Bergeron process, and Ostwald ripening. Nucleation starts inside the reorganized network, but crystals grow past it by direct condensation of the gas phase on their surface, driving liquid evaporation, and producing a network structure different from the original phase separation pattern. We argue that similar crystal-gel states can be formed in monatomic and molecular systems if the liquid phase is slow enough to induce viscoelastic phase separation, but fast enough to prevent immediate vitrification. This provides a novel pathway to form nanoporous crystals of metals and semiconductors without dealloying, which may be important for catalytic, optical, sensing, and filtration applications.

Disorder and excess modes in hard-sphere colloidal systems

The anomalous thermodynamic properties of glasses remain incompletely understood, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low-frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe a strong enhancement of low-frequency modes. Using a novel method (Zargar R. et al., Phys. Rev. Lett. 110 (2013) 258301) to determine the free energy, we also determine the entropy and the specific heat experimentally. It follows that the emergence of the excess modes and high values of the specific heat are directly related and are specific to the glass: even for solids containing a very large amount of defects, both the low-frequency density of states and the specific heat are significantly smaller than for the glass.

A possible four-phase coexistence in a single-component system

For different phases to coexist in equilibrium at constant temperature T and pressure P, the condition of equal chemical potential μ must be satisfied. This condition dictates that, for a single-component system, the maximum number of phases that can coexist is three. Historically this is known as the Gibbs phase rule, and is one of the oldest and venerable rules of thermodynamics. Here we make use of the fact that, by varying model parameters, the Gibbs phase rule can be generalized so that four phases can coexist even in single-component systems. To systematically search for the quadruple point, we use a monoatomic system interacting with a Stillinger–Weber potential with variable tetrahedrality. Our study indicates that the quadruple point provides flexibility in controlling multiple equilibrium phases and may be realized in systems with tunable interactions, which are nowadays feasible in several soft matter systems such as patchy colloids.

How to simulate patchy particles

Abstract.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.Graphical abstract