Note: Homogeneous TIP4P/2005 ice nucleation at low supercooling

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Thermodynamic origins of two-component multiphase condensates of proteins

Intracellular condensates are highly multi-component systems in which complex phase behaviour can ensue, including the formation of architectures comprising multiple immiscible condensed phases. Relying solely on physical intuition to manipulate such condensates is difficult because of the complexity of their composition, and systematically learning the underlying rules experimentally would be extremely costly. We address this challenge by developing a computational approach to design pairs of protein sequences that result in well-separated multilayered condensates and elucidate the molecular origins of these compartments. Our method couples a genetic algorithm to a residue-resolution coarse-grained protein model. We demonstrate that we can design protein partners to form multiphase condensates containing naturally occurring proteins, such as the low-complexity domain of hnRNPA1 and its mutants, and show how homo- and heterotypic interactions must differ between proteins to result in multiphasicity. We also show that in some cases the specific pattern of amino-acid residues plays an important role. Our findings have wide-ranging implications for understanding and controlling the organisation, functions and material properties of biomolecular condensates.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Faster Nucleation of Ice at the Three-Phase Contact Line: Influence of Interfacial Chemistry

Controlling the nucleation of ice is important in many areas including atmospheric sciences, cryopreservation, food science, and infrastructure protection. Presently, we conduct controlled experiments and analysis to uncover the influence of surface chemistry at the three-phase line on ice nucleation. We show that ice nucleation is faster upon replacing the air at the water-air interface with oils like silicone oil and almond oil. We show via statistically meaningful and carefully designed experiments that ice nucleation occurs at a higher temperature at an aluminum-water-silicone oil (or almond oil) interface as compared to an aluminum-water-air interface. We show that the location of ice nucleation can be controlled (in situations with multiple locations for ice nucleation) by controlling the interfacial chemistry at the three-phase line. We develop a model (which utilizes classical nucleation theory) to study the combined influence of two interfaces on a seed crystal of ice originating at the three-phase contact line. This model can evaluate the thermodynamic competition between nucleation at the three -phase line and heterogeneous nucleation at an interface. The model shows that three-phase contact lines usually result in a higher driving force than heterogeneous nucleation, which speeds up nucleation kinetics. Overall, our experiments and modeling uncover several useful insights into the influence of three-phase lines on nucleation during contact freezing.

Quantum-mechanical exploration of the phase diagram of water

The set of known stable phases of water may not be complete, and some of the phase boundaries between them are fuzzy. Starting from liquid water and a comprehensive set of 50 ice structures, we compute the phase diagram at three hybrid density-functional-theory levels of approximation, accounting for thermal and nuclear fluctuations as well as proton disorder. Such calculations are only made tractable because we combine machine-learning methods and advanced free-energy techniques. The computed phase diagram is in qualitative agreement with experiment, particularly at pressures ≲ 8000 bar, and the discrepancy in chemical potential is comparable with the subtle uncertainties introduced by proton disorder and the spread between the three hybrid functionals. None of the hypothetical ice phases considered is thermodynamically stable in our calculations, suggesting the completeness of the experimental water phase diagram in the region considered. Our work demonstrates the feasibility of predicting the phase diagram of a polymorphic system from first principles and provides a thermodynamic way of testing the limits of quantum-mechanical calculations.

Numerical calculation of free-energy barriers for entangled polymer nucleation

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.

Sea Spray Aerosol: Where Marine Biology Meets Atmospheric Chemistry

Atmospheric aerosols have long been known to alter climate by scattering incoming solar radiation and acting as seeds for cloud formation. These processes have vast implications for controlling the chemistry of our environment and the Earth's climate. Sea spray aerosol (SSA) is emitted over nearly three-quarters of our planet, yet precisely how SSA impacts Earth's radiation budget remains highly uncertain. Over the past several decades, studies have shown that SSA particles are far more complex than just sea salt. Ocean biological and physical processes produce individual SSA particles containing a diverse array of biological species including proteins, enzymes, bacteria, and viruses and a diverse array of organic compounds including fatty acids and sugars. Thus, a new frontier of research is emerging at the nexus of chemistry, biology, and atmospheric science. In this Outlook article, we discuss how current and future aerosol chemistry research demands a tight coupling between experimental (observational and laboratory studies) and computational (simulation-based) methods. This integration of approaches will enable the systematic interrogation of the complexity within individual SSA particles at a level that will enable prediction of the physicochemical properties of real-world SSA, ultimately illuminating the detailed mechanisms of how the constituents within individual SSA impact climate.

On the time required to freeze water

By using the seeding technique the nucleation rate for the formation of ice at room pressure will be estimated for the TIP4P/ICE model using longer runs and a smaller grid of temperatures than in the previous work. The growth rate of ice will be determined for TIP4P/ICE and for the mW model of water. Although TIP4P/ICE and mW have a similar melting point and melting enthalpy, they differ significantly in the dynamics of freezing. The nucleation rate of mW is lower than that of TIP4P/ICE due to its higher interfacial free energy. Experimental results for the nucleation rate of ice are between the predictions of these two models when obtained from the seeding technique, although closer to the predictions of TIP4P/ICE. The growth rate of ice for the mW model is four orders of magnitude larger than for TIP4P/ICE. Avrami's expression is used to estimate the crystallization time from the values of the nucleation and growth rates. For mW the minimum in the crystallization time is found at approximately 85 K below the melting point and its value is of about a few ns, in agreement with the results obtained from brute force simulations by Moore and Molinero. For the TIP4P/ICE the minimum is found at about 55 K below the melting point, but its value is about ten microseconds. This value is compatible with the minimum cooling rate required to avoid the formation of ice and obtaining a glass phase. The crossover from the nucleation controlled crystallization to the growth controlled crystallization will be discussed for systems of finite size. This crossover could explain the apparent discrepancy between the values of J obtained by different experimental groups for temperatures below 230 K and should be considered as an alternative hypothesis to the two previously suggested: internal pressure and/or surface freezing effects. A maximum in the compressibility was found for the TIP4P/ICE model in supercooled water. The relaxation time is much smaller than the crystallization time at the temperature at which this maximum occurs, so this maximum is a real thermodynamic feature of the model. At the temperature of minimum crystallization time, the crystallization time is larger than the relaxation time by just two orders of magnitude.

Hybrid Monte Carlo with LAMMPS

We describe a strategy for performing canonical and isothermal-isobaric ensemble hybrid Monte Carlo (HMC) simulations with the widely-used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics (MD) software package. The overall workflow for the HMC simulations is handled using an external Python driver script, which invokes LAMMPS’ library interface to perform numerically intensive tasks such as MD integration. We document several rigorous consistency checks that have been used to validate our HMC implementation. We also demonstrate that our approach can be readily extended to implement biased HMC sampling schemes for computing free energies. Codes and input files from the documented examples are available on the web.

Control of ice nucleation: freezing and antifreeze strategies

Water freezing remains a perennial topic of great relevance to many important aspects of our lives; from the climate to human society and from economics to medicine, frozen water profoundly influences our living environment and life activities.

Interfacial Free Energy as the Key to the Pressure-Induced Deceleration of Ice Nucleation

The avoidance of water freezing is the holy grail in the cryopreservation of biological samples, food, and organs. Fast cooling rates are used to beat ice nucleation and avoid cell damage. This strategy can be enhanced by applying high pressures to decrease the nucleation rate, but the physics behind this procedure has not been fully understood yet. We perform computer experiments to investigate ice nucleation at high pressures consisting in embedding ice seeds in supercooled water. We find that the slowing down of the nucleation rate is mainly due to an increase of the ice I-water interfacial free energy with pressure. Our work also clarifies the molecular mechanism of ice nucleation for a wide pressure range. This study is not only relevant to cryopreservation, but also to water amorphization and climate change modeling.

Molecular simulation of homogeneous nucleation of crystals of an ionic liquid from the melt

The homogeneous nucleation of crystals of the ionic liquid [dmim(+)][Cl(-)] from its supercooled liquid phase in the bulk (P = 1 bar, T = 340 K, representing a supercooling of 58 K) was studied using molecular simulations. The string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] was used in combination with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] to sketch a minimum free energy path connecting the supercooled liquid and the monoclinic crystal phases, and to determine the free energy and the rates involved in the homogeneous nucleation process. The physical significance of the configurations found along this minimum free energy path is discussed with the help of calculations based on classical nucleation theory and with additional simulation results obtained for a larger system. Our results indicate that, at a supercooling of 58 K, the liquid has to overcome a free energy barrier of the order of 60 kcal/mol and to form a critical nucleus with an average size of about 3.6 nm, before it reaches the thermodynamically stable crystal phase. A simulated homogeneous nucleation rate of 5.0 × 10(10) cm(-3) s(-1) was obtained for our system, which is in reasonable agreement with experimental and simulation rates for homogeneous nucleation of ice at similar degrees of supercooling. This study represents our first step in a series of studies aimed at understanding the nucleation and growth of crystals of organic salts near surfaces and inside nanopores.

Communication: On the stability of ice 0, ice i, and I(h)

Using ab initio methods, we examine the stability of ice 0, a recently proposed tetragonal form of ice implicated in the homogeneous freezing of water [J. Russo, F. Romano, and H. Tanaka, Nat. Mater. 13, 670 (2014)]. Vibrational frequencies are computed across the complete Brillouin Zone using Density Functional Theory (DFT), to confirm mechanical stability and quantify the free energy of ice 0 relative to ice I(h). The robustness of this result is tested via dispersion corrected semi-local and hybrid DFT, and Quantum Monte-Carlo calculation of lattice energies. Results indicate that popular molecular models only slightly overestimate the stability of ice zero. In addition, we study all possible realisations of proton disorder within the ice zero unit cell, and identify the ground state as ferroelectric. Comparisons are made to other low density metastable forms of ice, suggesting that the ice i structure [C. J. Fennel and J. D. Gezelter, J. Chem. Theory Comput. 1, 662 (2005)] may be equally relevant to ice formation.

Stacking disorder in ice I

Traditionally, ice I was considered to exist in two well-defined crystalline forms at ambient pressure: stable hexagonal ice (ice Ih) and metastable cubic ice (ice Ic). However, it is becoming increasingly evident that what has been called cubic ice in the past does not have a structure consistent with the cubic crystal system. Instead, it is a stacking-disordered material containing cubic sequences interlaced with hexagonal sequences, which is termed stacking-disordered ice (ice Isd). In this article, we summarise previous work on ice with stacking disorder including ice that was called cubic ice in the past. We also present new experimental data which shows that ice which crystallises after heterogeneous nucleation in water droplets containing solid inclusions also contains stacking disorder even at freezing temperatures of around -15 °C. This supports the results from molecular simulations, that the structure of ice that crystallises initially from supercooled water is always stacking-disordered and that this metastable ice can transform to the stable hexagonal phase subject to the kinetics of recrystallization. We also show that stacking disorder in ice which forms from water droplets is quantitatively distinct from ice made via other routes. The emerging picture of ice I is that of a very complex material which frequently contains stacking disorder and this stacking disorder can vary in complexity depending on the route of formation and thermal history.

Classical nucleation theory of homogeneous freezing of water: thermodynamic and kinetic parameters

Different formulations of the kinetic and thermodynamic parameters of CNT are evaluated against measured nucleation rates.