Accurate estimate of nucleation rate is crucial for the study of ice nucleation and ice-promoting/anti-freeze strategies. Within the framework of Classical Nucleation Theory (CNT), the estimate of ice nucleation rate is very sensitive to thermodynamic parameters, such as chemical potential difference between water and ice $Δμ$ and ice-water interfacial free energy $γ$. However, even today, there are still many contradictions and approximations in the estimating of these thermodynamic parameters, introducing large uncertainty to the estimate of the ice nucleation rate. Herein, starting from the basic concepts, for a general solid-liquid crystallization system, we expand the Gibbs-Thomson (GT) equation to second order, and derive the second-order analytical formulas of $Δμ$, $γ$ and nucleation barrier $ΔG$ with combining molecular dynamics (MD) simulations. These formulas describe well the temperature dependence of these thermodynamic parameters. Our results can provide a method of estimating $Δμ$, $γ$ and $ΔG$.
We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a Seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mole per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations we combine Seeding with the direc…
We investigate with computer simulations the effect of applying an electric field on the water-to-ice transition. We use a combination of state-of-the-art simulation techniques to obtain phase boundaries and crystal growth rates (direct coexistence), nucleation rates (seeding) and interfacial free energies (seeding and mold integration). First, we consider ice Ih, the most stable polymorph in the absence of a field. Its normal melting temperature, speed of crystal growth and nucleation rate (for a given supercooling) diminish as the intensity of the field goes up. Then, we study polarised cubi…
To predict the radiative forcing of clouds it is necessary to know the rate with which ice homogeneously nucleates in supercooled water. Such rate is often measured in drops to avoid the presence of impurities. At large supercooling small (nanoscopic) drops must be used to prevent simultaneous nucleation events. The pressure inside such drops is larger than the atmospheric one by virtue of the Laplace equation. In this work, we take into account such pressure raise in order to predict the nucleation rate in droplets using the TIP4P/Ice water model. We start from a recent estimate of the maximu…
Ice formation is one of the most common and important processes on earth and almost always occurs at the surface of a material. A basic understanding of how the physicochemical properties of a material's surface affect its ability to form ice has remained elusive. Here, we use molecular dynamics simulations to directly probe heterogeneous ice nucleation at a hexagonal surface of a nanoparticle of varying hydrophilicity. Surprisingly, we find that structurally identical surfaces can both inhibit and promote ice formation and analogous to a chemical catalyst, it is found that an optimal interact…
The solidification behaviour of suspensions of alumina particles during directional solidification is investigated here by in situ observations using X-ray radiography and tomography. The objective of this study is to assess the influence of particle size on the solidification behaviour of the suspensions during the early stages of solidification. Four powders with particle size in the range 0.2-3.4μm (median size) were investigated. Solidification is obtained by cooling at a constant rate, starting from room temperature. Attention is specifically paid to the nucleation and growth behaviour of…
Organic molecules such as steroids or amino acids form crystals that can facilitate the formation of ice -- arguably the most important phase transition on earth. However, the origin of the ice nucleating ability of organic crystals is still largely unknown. Here, we combine experiments and simulations to unravel the microscopic details of ice formation on cholesterol, a prototypical organic crystal widely used in cryopreservation. We find that cholesterol -- which is also a substantial component of cell membranes -- is an ice nucleating agent more potent than many inorganic substrates, includ…
Ice formation is ubiquitous in nature, with important consequences in a variety of environments, including biological cells, soil, aircraft, transportation infrastructure and atmospheric clouds. However, its intrinsic kinetics and microscopic mechanism are difficult to discern with current experiments. Molecular simulations of ice nucleation are also challenging, and direct rate calculations have only been performed for coarse-grained models of wate. For molecular models, only indirect estimates have been obtained, e.g. by assuming the validity of classical nucleation theory. We use a path sam…
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, especially at negative pressure conditions. Our results suggest a peculiar non-monotonic temperature dependence of liquid-vapor surface tension at temperatures where liquid-vapor coexistence is metastable with respect …
Ice nucleation is a process of great relevance in physics, chemistry, technology and environmental sciences, much theoretical and experimental efforts have been devoted to its understanding, but still it remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom TIP4P/Ice model, and the features of the critical nucleus…
Acoustic cavitation is known to trigger ice nucleation in supercooled water. Several competing and still debatable mechanisms have been proposed in the literature and are related to the pressure field in the vicinity of the bubble at the end of its collapse. Numerical simulations of the bubble dynamics show that during the bubble expansions in the bounces following the main collapse, the bubble core temperature reaches values far below 0 °C for time periods of about 500 ns. The water vapour present in the bubble during these time intervals explores the liquid and the solid region of the phase …
What makes a material a good ice nucleating agent? Despite the importance of heterogeneous ice nucleation to a variety of fields, from cloud science to microbiology, major gaps in our understanding of this ubiquitous process still prevent us from answering this question. In this work, we have examined the ability of generic crystalline substrates to promote ice nucleation as a function of the hydrophobicity and the morphology of the surface. Nucleation rates have been obtained by brute-force molecular dynamics simulations of coarse-grained water on top of different surfaces of a model fcc crys…
Hydrodynamic flow can have complex and far-reaching consequences on the rate of homogenous nucleation. We present a general formalism for calculating the nucleation rates of simply sheared systems. We have derived an extension to the conventional Classical Nucleation Theory, explicitly embodying the shear rate. Seeded Molecular Dynamics simulations form the backbone of our approach. The framework can be used for moderate supercoolings, at which temperatures brute-force methods are practically infeasible. The competing energetic and kinetic effects of shear arise naturally from the equations. W…
Water is one of the most abundant substances on Earth, and ice, i.e., solid water, has more than 18 known phases. Normally ice in nature exists only as Ice Ih, Ice Ic, or a stacking disordered mixture of both. Although many theoretical efforts have been devoted to understanding the thermodynamics of different ice phases at ambient temperature and pressure, there still remains many puzzles. We simulated the reversible transitions between water and different ice phases by performing full atom molecular dynamics simulations. Using the enhanced sampling method MetaITS with the two selected X-ray d…
Crystallization from a supercooled liquid initially proceeds via the formation of a small solid embryo (nucleus), which requires surmounting an activation barrier. This phenomenon is most easily studied by numerical simulation, using specialized biased-sampling techniques to overcome the limitations imposed by the rarity of nucleation events. Here, I focus on the barrier to homogeneous ice nucleation in supercooled water, as represented by the monatomic-water model, which in the bulk exhibits a complex interplay between different ice structures. I consider various protocols to identify solidli…
In this work, we evaluate by means of computer simulations the rate for ice homogeneous nucleation for several water models such as TIP4P, TIP4P/2005,TIP4P/ICE, and mW (following the same procedure as in Sanz et al. [J. Am. Chem. Soc.135, 15008 (2013)]) in a broad temperature range. We estimate the ice-liquid interfacial free-energy, and conclude that for all water models γ decreases as the temperature decreases. Extrapolating our results to the melting temperature, we obtain a value of the interfacial free-energy between 25 and 32 mN/m in reasonable agreement with the reported experimental va…
Among all the freezing transitions, that of water into ice is probably the most relevant to biology, physics, geology or atmospheric science. In this work we investigate homogeneous ice nucleation by means of computer simulations. We evaluate the size of the critical cluster and the nucleation rate for temperatures ranging between 15K and 35K below melting. We use the TIP4P/2005 and the TIP4P/Ice water models. Both give similar results when compared at the same temperature difference with the model's melting temperature. The size of the critical cluster varies from $\sim$8000 molecules (radius…
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) li…
Models without an explicit time dependence, called singular models, are widely used for fitting the distribution of temperatures at which water droplets freeze. In 1950 Levine developed the original singular model. His key assumption was that each droplet contained many nucleation sites, and that freezing occurred due to the nucleation site with the highest freezing temperature. The fact that freezing occurs due to the maximum value out of large number of nucleation temperatures, means that we can apply the results of what is called extreme-value statistics. This is the statistics of the extre…
The critical radius of a nucleus grown by diffusion in a solution is studied thermodynamically as well as kinetically. The thermodynamic growth equation called Zeldovich equation of classical nucleation theory (CNT) and the kinetic diffusional growth equation combined with the Ostwald-Freundlich boundary condition lead to the same critical radius. However, it should be pointed out that the diffusional equation may lead to a kinetic critical radius that is different from the thermodynamic critical radius, thus indicating the possibility of kinetically controlling the critical radius of a nucleu…
Hypothesis: As a fluid approaches three phase coexistence, adsorption may take place by the successive formation of two intervening wetting films. The equilibrium thickness of these wetting layers is the result of a delicate balance of intermolecular forces, as dictated by an underlying interface potential. The van der Waals forces for the two variable adsorption layers may be formulated exactly from Dzyaloshinskii-Lifshitz-Pitaevskii theory, and analytical approximations may be derived that extent well beyond the validity of conventional Hamaker theory. Calculations: We consider the adsorptio…
A long controversy of ice lensing exists in the research of frost heave. By elucidating the mechanical and thermodynamics equilibria at the interface, we present the thermodynamics of the water/ice interface from macroscale to microscale for the freezing of colloidal suspensions. The application of the Clapeyron equation is confirmed both at macroscale to microscale via curvature effect. The thermodynamics at the interface indicates the initial of ice lensing/banding from the growth of pore ice, determined by the critical curvature undercooling instead of the critical fracture of frozen fringe…
We analyze the rotational demagnetization of artificial spin ice, a recently realized array of nanoscale single-domain ferromagnetic islands. Demagnetization does not anneal this model system into its anti-ferromagnetic ground state: the moments have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal system has an effective extensive degeneracy and we introduce a formalism that can predict the populations of local states in this ice-like system with no adjustable parameters.
Combining three numerical methods (forward flux sampling, seeding of droplets, and finite size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extr…
Contact freezing is a mode of atmospheric ice nucleation in which a collision between a dry ice nucleating particle (INP) and a water droplet results in considerably faster heterogeneous nucleation. The molecular mechanism of such enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface. By simulating heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids, we demonstrate t…
A long standing problem of domain switching process - how domains nucleate - is examined in ultrathin ferroelectric films. We demonstrate that the large depolarization fields in ultrathin films could significantly lower the nucleation energy barrier (U*) to a level comparable to thermal energy (kBT), resulting in power-law like polarization decay behaviors. The "Landauer's paradox": U* is thermally insurmountable is not a critical issue in the polarization switching of ultrathin ferroelectric films. We empirically find a universal relation between the polarization decay behavior and U*/kBT.
In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for groundstate configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.
The multivariable theory of nucleation [J. Chem. Phys. 124, 124512 (2006)] is applied to the problem of vapor bubbles formation in pure liquids. The presented self-consistent macroscopic theory of this process employs thermodynamics (classical, statistical and linear non-equilibrium), hydrodynamics and interfacial kinetics. As a result of thermodynamic study of the problem, the work of formation of a bubble is obtained and parameters of the critical bubble are determined. The variables V (the bubble volume), ρ(the vapor density), and T (the vapor temperature) are shown to be natural for the gi…
One of most intriguing problems of heterogeneous crystal nucleation in droplets is its strong enhancement in the contact mode (when the foreign particle is presumably in some kind of contact with the droplet surface) compared to the immersion mode (particle immersed in the droplet). Many heterogeneous centers have different nucleation thresholds when they act in contact or immersion modes, indicating that the mechanisms may be actually different for the different modes. Underlying physical reasons for this enhancement have remained largely unclear. In this paper we present a model for the ther…
A widely spread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. Nucleation process, polymorph selection, and crystal habits depend crucially on this thermodynamic parameter. When performing simulations in the canonical ensemble as the crystalline phase is deposited the solution is depleted of solutes. This unavoidable modification of the thermodynamic conditions leads to significant artifact. Here we adopt the idea of the constant chemical potential molecular dynamics approach of…
Supercooled water is a metastable phase of liquid water below the melting temperature. An interesting discussion recently developed on the relationship between crystallization rate and the time scales of equilibration within the liquid phase. Calculations using a coarse grained monatomic model of water, the mW model, suggested that equilibration of the liquid below the temperature of homogeneous nucleation $T_H\approx225$ K is slower than ice nucleation. Here, a 3 $μ$s long molecular dynamics simulation of the TIP4P-Ew water model is presented to investigate the relaxation properties of an ato…
Despite the exponential growth in computing resources and the availability of a myriad of different theoretical water models, an accurate, yet computationally efficient molecular level description of mesoscopic grain growth remains a grand challenge. The underlying phase transitions and dynamical processes in deeply supercooled systems are often rendered inaccessible due to limitations imposed by system sizes and timescales, which is further compounded by their sluggish kinetics. Here, we introduce a machine-learned, bond-order-based potential model (BOP) that more accurately describes the ano…
One of water's unsolved puzzles is the question of what determines the lowest temperature to which it can be cooled before freezing to ice. The supercooled liquid has been probed experimentally to near the homogeneous nucleation temperature TH{\approx}232 K, yet the mechanism of ice crystallization - including the size and structure of critical nuclei - has not yet been resolved. The heat capacity and compressibility of liquid water anomalously increase upon moving into the supercooled region according to a power law that would diverge at Ts{\approx}225 K,(1,2) so there may be a link between w…
Nonequilibrium thermodynamics formalism is proposed to derive the flux of grainy (bubbles-containing) matter, emerging in a nucleation growth process. Some power and non-power limits, due to the applied potential as well as owing to basic correlations in such systems, have been discussed. Some encouragement for such a discussion comes from the fact that the nucleation and growth processes studied, and their kinetics, are frequently reported in literature as self-similar (characteristic of algebraic correlations and laws) both in basic entity (grain; bubble) size as well as time scales.
In recent decades, computer simulations have found increasingly widespread use as powerful tools of studying phase transitions in wide variety of systems. In the particular and very important case of aqueous systems, the commonly used force-fields tend to offer quite different predictions with respect to a wide range of thermodynamic and kinetic properties, including the ease of ice nucleation, the propensity to freeze at a vapor-liquid interface, and the existence of a liquid-liquid phase transition. It is thus of fundamental and practical interest to understand how different features of a gi…
We determine the non-equilibrium grain size distribution during the crystallization of a solid in $d$ dimensions at fixed thermodynamic conditions, for the random nucleation and growth model, and in absence of grain coalescence. Two distinct generalizations of the theory established earlier are considered. A closed analytic expression of the grain size distribution useful for experimental studies is derived for anisotropic growth rates. The main difference from the isotropic growth case is the appearance of a constant prefactor in the distribution. The second generalization considers a Gaussia…
In this study, molecular dynamic simulations are employed to investigate the nucleation of NaCl crystal in solutions. According to the simulations, the dissolved behaviors of NaCl in water are dependent on ion concentrations. With increasing NaCl concentrations, the dissolved Na$^+$ and Cl$^-$ ions tend to be aggregated in solutions. In combination with our recent studies, the aggregate of dissolved solutes is mainly ascribed to the hydrophobic interactions. Thermodynamically, no barrier is needed to overcome in the formation of the solute aggregate. This is different from the two-step nucleat…
Motivated by recent experiments showing the promise of noble gases as cryoprotectants, we perform molecular dynamics modeling of phase transitions in water with xenon under cooling. We study the structure and dynamics of xenon water solution as a function of temperature. Homogeneous nucleation of clathrate hydrate phase is observed and characterized. As the temperature is further reduced we observe hints of dissociation of clathrate due to stronger hydrophobic hydration, pointing towards a possible instability of clathrate at cryogenic temperatures and conversion to an amorphous phase comprise…
With numerical simulations of the mW model of water, we investigate the energetic stability of crystalline clusters for both Ice I (cubic and hexagonal ice) and for the metastable Ice 0 phase as a function of the cluster size. Under a large variety of forming conditions, we find that the most stable cluster changes as a function of size: at small sizes the Ice 0 phase produces the most stable clusters, while at large sizes there is a crossover to Ice I clusters. We further investigate the growth of crystalline clusters with the seeding technique and study the growth patterns of different cryst…
Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process as well as correctly calculating the relative free energies of different polymorphs. Here we demonstrate, for the prototypical case of urea nucleation from melt, how one can learn such a 1-dimensional reaction coordinate as a function of pre-specified order parameters, and use it to perform efficient biased all-atom molecular dynamics simulations. The r…
Finite size artifacts arise in molecular simulations of nucleation when critical nuclei are too close to their periodic images. A rigorous determination of what constitutes too close is, however, a major challenge. Recently, we devised rigorous heuristics for detecting such artifacts based on our investigation of how system size impacts the rate of heterogeneous ice nucleation (Hussain, Haji-Akbari, \emph{J. Chem. Phys.} \textbf{154}, 014108, \textbf{2021}). We identified the prevalence of critical nuclei spanning across the periodic boundary, and the thermodynamic and structural properties of…
