Seeding approach to crystal nucleation

Microscopic mechanism of water-assisted diffusional phase transitions in inorganic metal halide perovskites

The stability of perovskite materials is profoundly influenced by the presence of moisture in the surrounding environment. While it is well-established that water triggers and accelerates the black-yellow phase transition, leading to the degradation of the photovoltaic properties of perovskites, the underlying microscopic mechanism remains elusive. In this study, we employ classical molecular dynamics simulations to examine the role of water molecules in the yellow-black phase transition in a typical inorganic metal halide perovskite, CsPbI3. We have demonstrated, through interfacial energy calculations and classical nucleation theory, that the phase transition necessitates a crystal-amorphous-crystal two-step pathway rather than the conventional crystal-crystal mechanism. Simulations for CsPbI3 nanowires show that water molecules in the air can enter the amorphous interface between the black and yellow regions. The phase transition rate markedly increases with the influx of interfacial water molecules, which enhance ion diffusivity by reducing the diffusion barrier, thereby expediting the yellow-black phase transition in CsPbI3. We propose a general mechanism through which solvent molecules can greatly facilitate phase transitions that otherwise have prohibitively high transition energies.

Re-entrant percolation in active Brownian hard disks

Non-equilibrium clustering and percolation are investigated in an archetypal model of two-dimensional active matter using dynamic simulations of self-propelled Brownian repulsive particles. We concentrate on the single-phase region up to moderate levels of activity, before motility-induced phase separation (MIPS) sets in. Weak activity promotes cluster formation and lowers the percolation threshold. However, driving the system further out of equilibrium partly reverses this effect, resulting in a minimum in the critical density for the formation of system-spanning clusters and introducing re-entrant percolation as a function of activity in the pre-MIPS regime. This non-monotonic behaviour arises from competition between activity-induced effective attraction (which eventually leads to MIPS) and activity-driven cluster breakup. Using an adapted iterative Boltzmann inversion method, we derive effective potentials to map weakly active cases onto a passive (equilibrium) model with conservative attraction, which can be characterised by Monte Carlo simulations. While the active and passive systems have practically identical radial distribution functions, we find decisive differences in higher-order structural correlations, to which the percolation threshold is highly sensitive. For sufficiently strong activity, no passive pairwise potential can reproduce the radial distribution function of the active system.

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.

Hydrogen-bond linking is crucial for growing ice VII embryos

We use molecular dynamics simulations to examine the homogeneous nucleation of ice VII from metastable liquid water. An unsupervised machine learning classification identifies two distinct local structures composing Ice VII nuclei. The seeding method, combined with the classical nucleation theory (CNT), predicts the solid-liquid interfacial free energy, consistent with the value from the mold integration method. Meanwhile, the nucleation rates estimated from the CNT framework and brute force spontaneous nucleations are inconsistent, and we discuss the reasons for this discrepancy. Structural and dynamical heterogeneities suggest that the potential birthplace for an ice VII embryo is relatively ordered, although not necessarily relatively immobile. Moreover, we demonstrate that without the formation of hydrogen-bond links, ice VII embryos do not grow.

Finding the differences: Classical nucleation perspective on homogeneous melting and freezing of hard spheres

By employing brute-force molecular dynamics, umbrella sampling, and seeding simulations, we investigate homogeneous nucleation during melting and freezing of hard spheres. We provide insights into these opposing phase transitions from the standpoint of classical nucleation theory. We observe that melting has both a lower driving force and a lower interfacial tension than freezing. The lower driving force arises from the vicinity of a spinodal instability in the solid and from a strain energy. The lower interfacial tension implies that the Tolman lengths associated with melting and freezing have opposite signs, a phenomenon that we interpret with Turnbull's rule. Despite these asymmetries, the nucleation rates for freezing and melting are found to be comparable.

Current State and Future Perspectives of Printable Organic and Perovskite Solar Cells

Photovoltaic technology presents a sustainable solution to address the escalating global energy consumption and a reliable strategy for achieving net-zero carbon emissions by 2050. Emerging photovoltaic technologies, especially the printable organic and perovskite solar cells, have attracted extensive attention due to their rapidly transcending power conversion efficiencies and facile processability, providing great potential to revolutionize the global photovoltaic market. To accelerate these technologies to translate from the laboratory scale to the industrial level, it is critical to develop well-defined and scalable protocols to deposit high-quality thin films of photoactive and charge-transporting materials. Herein, the current state of printable organic and perovskite solar cells is summarized and the view regarding the challenges and prospects toward their commercialization is shared. Different printing techniques are first introduced to provide a correlation between material properties and printing mechanisms, and the optimization of ink formulation and film-formation during large-area deposition of different functional layers in devices are then discussed. Engineering perspectives are also discussed to analyze the criteria for module design. Finally, perspectives are provided regarding the future development of these solar cells toward practical commercialization. It is believed that this perspective will provide insight into the development of printable solar cells and other electronic devices.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

The limit of macroscopic homogeneous ice nucleation at the nanoscale

Nucleation in small volumes of water has garnered renewed interest due to the relevance of pore condensation and freezing under conditions of low partial pressures of water, such as in the upper troposphere. Molecular simulations can in principle provide insight on this process at the molecular scale that is challenging to achieve experimentally. However, there are discrepancies in the literature as to whether the rate in confined systems is enhanced or suppressed relative to bulk water at the same temperature and pressure. In this study, we investigate the extent to which the size of the critical nucleus and the rate at which it grows in thin films of water are affected by the thickness of the film. Our results suggest that nucleation remains bulk-like in films that are barely large enough accommodate a critical nucleus. This conclusion seems robust to the presence of physical confining boundaries. We also discuss the difficulties in unambiguously determining homogeneous nucleation rates in nanoscale systems, owing to the challenges in defining the volume. Our results suggest any impact on a film's thickness on the rate is largely inconsequential for present day experiments.

Crystallization of FAPbI3: Polytypes and stacking faults

Molecular dynamics simulations are performed to study the crystallization of formamidinium lead iodide. From all-atom simulations of the crystal growth process and the δ-α-phase transitions, we try to reveal the formation of various stack-faulted intermediate defected structures and report various polytypes of formamidinium lead iodide that are observed from simulations.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Brute-force nucleation rates of hard spheres compared with rare-event methods and classical nucleation theory

We determine nucleation rates of hard spheres using brute-force molecular dynamics simulations. We overcome nucleation barriers of up to 28 kBT, leading to a rigorous test of nucleation rates obtained from rare-event methods and classical nucleation theory. Our brute-force nucleation rates show excellent agreement with umbrella sampling simulations by Filion et al. [J. Chem. Phys. 133, 244115 (2010)] and seeding simulations by Espinosa et al. [J. Chem. Phys. 144, 034501 (2016)].

Anisotropic Collective Variables with Machine Learning Potential for Ab Initio Crystallization of Complex Ceramics

Enhanced sampling molecular dynamics (MD) simulations have been extensively used in the phase transition study of simple crystalline materials, such as aluminum, silica, and ice. However, MD simulation of the crystallization process for complex crystalline materials still faces a formidable challenge due to their multicomponent induced multiphase problem. Here, we realize the ab initio accuracy MD crystallization simulations of complex ceramics by using anisotropic collective variables (CVs) and machine learning (ML) potential. The anisotropic X-ray diffraction intensity CVs provide precise identification of complex crystal structures with detailed crystallography information, while the ML potential makes it feasible to further perform enhanced sampling simulations with ab initio accuracy. We verify the universality and accuracy of this method through complex ceramics with three kinds of representative structures, i.e., Ti3SiC2 for the MAX structure, zircon for the mineral structure, and lead zirconate titanate for the perovskite structure. It demonstrates exceptional efficiency and ab initio quality in achieving crystallization and generating free energy surfaces of all these ceramics, facilitating the analysis and design of complex crystalline materials.

Characterizing Surface Ice-Philicity Using Molecular Simulations and Enhanced Sampling

The formation of ice, which plays an important role in diverse contexts ranging from cryopreservation to atmospheric science, is often mediated by solid surfaces. Although surfaces that interact favorably with ice (relative to liquid water) can facilitate ice formation by lowering nucleation barriers, the molecular characteristics that confer icephilicity to a surface are complex and incompletely understood. To address this challenge, here we introduce a robust and computationally efficient method for characterizing surface ice-philicity that combines molecular simulations and enhanced sampling techniques to quantify the free energetic cost of increasing surface-ice contact at the expense of surface-water contact. Using this method to characterize the ice-philicity of a family of model surfaces that are lattice matched with ice but vary in their polarity, we find that the nonpolar surfaces are moderately ice-phobic, whereas the polar surfaces are highly ice-philic. In contrast, for surfaces that display no complementarity to the ice lattice, we find that ice-philicity is independent of surface polarity and that both nonpolar and polar surfaces are moderately ice-phobic. Our work thus provides a prescription for quantitatively characterizing surface ice-philicity and sheds light on how ice-philicity is influenced by lattice matching and polarity.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

Solubility of carbon dioxide in water: Some useful results for hydrate nucleation

In this paper, the solubility of carbon dioxide (CO2) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and the TraPPE model for CO2. In particular, the solubility of CO2 in water when in contact with the CO2 liquid phase and the solubility of CO2 in water when in contact with the hydrate have been determined. The solubility of CO2 in a liquid-liquid system decreases as the temperature increases. The solubility of CO2 in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar (T3). We compare the predictions with T3 obtained using the direct coexistence technique in a previous work. The results of both methods agree, and we suggest 290(2) K as the value of T3 for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrates along the isobar. The new approach is based on the use of the solubility curve of CO2 when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO2, providing reliable values for the driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of dispersive interactions and the occupancy of CO2 on the driving force for nucleation of the hydrate.

Are Neural Network Potentials Trained on Liquid States Transferable to Crystal Nucleation? A Test on Ice Nucleation in the mW Water Model

Neural network potentials (NNPs) are increasingly being used to study processes that happen on long time scales. A typical example is crystal nucleation, which rate is controlled by the occurrence of a rare fluctuation, i.e., the appearance of the critical nucleus. Because the properties of this nucleus are far from those of the bulk crystal, it is yet unclear whether NN potentials trained on equilibrium liquid states can accurately describe nucleation processes. So far, nucleation studies on NNPs have been limited to ab initio models whose nucleation properties are unknown, preventing an accurate comparison. Here we train a NN potential on the mW model of water─a classical three-body potential whose nucleation time scale is accessible in standard simulations. We show that a NNP trained only on a small number of liquid state points can reproduce with great accuracy the nucleation rates and free energy barriers of the original model, computed from both spontaneous and biased trajectories, strongly supporting the use of NNPs to study nucleation events.

RSeeds: Rigid Seeding Method for Studying Heterogeneous Crystal Nucleation

Heterogeneous nucleation is the dominant form of liquid-to-solid transition in nature. Although molecular simulations are most uniquely suited to studying nucleation, the waiting time to observe even a single nucleation event can easily exceed the current computational capabilities. Therefore, there exists an imminent need for methods that enable computationally fast and feasible studies of heterogeneous nucleation. Seeding is a technique that has proven to be successful at dramatically expanding the range of computationally accessible nucleation rates in simulation studies of homogeneous crystal nucleation. In this article, we introduce a new seeding method for heterogeneous nucleation called Rigid Seeding (RSeeds). Crystalline seeds are treated as pseudorigid bodies and simulated on a surface with metastable liquid above its melting temperature. This allows the seeds to adapt to the surface and identify favorable seed-surface configurations, which is necessary for reliable predictions of crystal polymorphs that form and the corresponding heterogeneous nucleation rates. We demonstrate and validate RSeeds for heterogeneous ice nucleation on a flexible self-assembled monolayer surface, a mineral surface based on kaolinite, and two model surfaces. RSeeds predicts the correct ice polymorph, exposed crystal plane, and rotation on the surface. RSeeds is semiquantitative and can be used to estimate the critical nucleus size and nucleation rate when combined with classical nucleation theory. We demonstrate that RSeeds can be used to evaluate nucleation rates spanning many orders of magnitude.

The water cavitation line as predicted by the TIP4P/2005 model

The formation of vapor bubbles in a metastable liquid, cavitation, is an activated process due to the free energy cost of having both phases at contact. Such an energetic penalty enables the existence of the liquid beyond its thermodynamic borders. Establishing the stability limits of a liquid as ubiquitous as water has important practical implications and has thereby attracted a lot of attention. Different experimental strategies and theoretical analyses have been employed to measure and predict the cavitation line, or the pressure-temperature kinetic stability border of liquid water. Understanding the location of the cavitation line requires knowing the cavitation rate dependence on pressure and temperature. Such dependency is difficult to obtain in experiments, and we use molecular simulations with the TIP4P/2005 model to fill this gap. By deeply overstretching liquid water below the saturation pressure, we are able to observe and quantify spontaneous cavitation. To deal with a lower overstretching regime, we resort to the Seeding technique, which consists of analyzing simulations of a liquid containing a vapor bubble under the theoretical framework of Classical Nucleation Theory. Combining spontaneous cavitation with Seeding, we get a wide overview of the cavitation rate. We study two different temperatures (450 and 550 K) and complement our perspective with the results previously obtained at 296.4 K [Menzl et al., Proc. Natl. Acad. Sci. 113, 13582 (2016)] to establish a broad simulation-experiment comparison. We find a good agreement between simulations and both isobaric heating and isochoric cooling experiments using quartz inclusions. We are, however, unable to reconcile simulations with other experimental techniques. Our results predict a decrease in the solid-liquid interfacial free energy as the liquid becomes increasingly overstretched with a temperature independent Tolman length of 0.1 nm. Therefore, the capillarity approximation underestimates the nucleation rate. Nonetheless, it provides a fair indication of the location of the cavitation line given the steep rate vs pressure dependence. Overall, our work provides a comprehensive view of the water cavitation phenomenon and sets an efficient strategy to investigate it with molecular simulations.

Minimum in the pressure dependence of the interfacial free energy between ice Ih and water

Despite the importance of ice nucleation, this process has been barely explored at negative pressures. Here, we study homogeneous ice nucleation in stretched water by means of molecular dynamics seeding simulations using the TIP4P/Ice model. We observe that the critical nucleus size, interfacial free energy, free energy barrier, and nucleation rate barely change between isobars from -2600 to 500 bars when they are represented as a function of supercooling. This allows us to identify universal empirical expressions for homogeneous ice nucleation in the pressure range from -2600 to 500 bars. We show that this universal behavior arises from the pressure dependence of the interfacial free energy, which we compute by means of the mold integration technique, finding a shallow minimum around -2000 bars. Likewise, we show that the change in the interfacial free energy with pressure is proportional to the excess entropy and the slope of the melting line, exhibiting in the latter a reentrant behavior also at the same negative pressure. Finally, we estimate the excess internal energy and the excess entropy of the ice Ih-water interface.

Homogeneous nucleation rate of methane hydrate formation under experimental conditions from seeding simulations

In this work, we shall estimate via computer simulations the homogeneous nucleation rate for the methane hydrate at 400 bars for a supercooling of about 35 K. The TIP4P/ICE model and a Lennard-Jones center were used for water and methane, respectively. To estimate the nucleation rate, the seeding technique was employed. Clusters of the methane hydrate of different sizes were inserted into the aqueous phase of a two-phase gas-liquid equilibrium system at 260 K and 400 bars. Using these systems, we determined the size at which the cluster of the hydrate is critical (i.e., it has 50% probability of either growing or melting). Since nucleation rates estimated from the seeding technique are sensitive to the choice of the order parameter used to determine the size of the cluster of the solid, we considered several possibilities. We performed brute force simulations of an aqueous solution of methane in water in which the concentration of methane was several times higher than the equilibrium concentration (i.e., the solution was supersaturated). From brute force runs, we infer the value of the nucleation rate for this system rigorously. Subsequently, seeding runs were carried out for this system, and it was found that only two of the considered order parameters were able to reproduce the value of the nucleation rate obtained from brute force simulations. By using these two order parameters, we estimated the nucleation rate under experimental conditions (400 bars and 260 K) to be of the order of log₁₀ (J/(m³ s)) = -7(5).

Free energy of critical droplets-from the binodal to the spinodal

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo in the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT), this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at 2.5σ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results for critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to the second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible regions. However, it is imprecise for the smallest droplets and largest metastabilities since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of the formation of critical droplets for the entire metastability range and all temperatures examined and deviates from density gradient theory by less than one k_BT.

Direct Calculation of the Interfacial Free Energy between NaCl Crystal and Its Aqueous Solution at the Solubility Limit

Salty water is the most abundant electrolyte aqueous mixture on Earth, however, very little is known about the NaCl-saturated solution interfacial free energy (γ_{s}). Here, we provide the first direct estimation of γ_{s} for several NaCl crystallographic planes by means of the mold integration technique, a highly efficient computational method to evaluate interfacial free energies with anisotropic crystal resolution. Making use of the JC-SPC/E model, one of the most benchmarked force fields for NaCl water solutions, we measure γ_{s} of four different crystal planes, (100), (110), (111), and (112[over ¯]) with the saturated solution at normal conditions. We find high anisotropy between the different crystal orientations with values ranging from 100 to 150  mJ m^{-2}, and the average value of the distinct planes being γ[over ¯]_{s}=137(20)  mJ m^{-2}. This value for the coexistence interfacial free energy is in reasonable agreement with previous extrapolations from nucleation studies. Our Letter represents a milestone in the computational calculation of interfacial free energies between ionic crystals and aqueous solutions.

Homogeneous nucleation of crystalline methane hydrate in molecular dynamics transition paths sampled under realistic conditions

Methane hydrates are important from a scientific and industrial perspective, and form by nucleation and growth from a supersaturated aqueous solution of methane. Molecular simulation is able to shed light on the process of homogeneous nucleation of hydrates, using straightforward molecular dynamics or rare event enhanced sampling techniques with atomistic and coarse grained force fields. In our previous work [Arjun, T. A. Berendsen, and P. G. Bolhuis, Proc. Natl. Acad. Sci. U. S. A. 116, 19305 (2019)], we performed transition path sampling (TPS) simulations using all atom force fields under moderate driving forces at high pressure, which enabled unbiased atomistic insight into the formation of methane hydrates. The supersaturation in these simulations was influenced by the Laplace pressure induced by the spherical gas reservoir. Here, we investigate the effect of removing this influence. Focusing on the supercooled, supersaturated regime to keep the system size tractable, our TPS simulations indicate that nuclei form amorphous structures below roughly 260 K and crystalline sI structures above 260 K. For these temperatures, the average transition path lengths are significantly longer than in our previous study, pushing the boundaries of what can be achieved with TPS. The temperature to observe a critical nucleus of certain size was roughly 20 K lower compared to a spherical reservoir due to the lower concentration of methane in the solution, yielding a reduced driving force. We analyze the TPS results using a model based on classical nucleation theory. The corresponding free energy barriers are estimated and found to be consistent with previous predictions, thus adding to the overall picture of the hydrate formation process.

Solubility of Methane in Water: Some Useful Results for Hydrate Nucleation

In this paper, the solubility of methane in water along the 400 bar isobar is determined by computer simulations using the TIP4P/Ice force field for water and a simple LJ model for methane. In particular, the solubility of methane in water when in contact with the gas phase and the solubility of methane in water when in contact with the hydrate has been determined. The solubility of methane in a gas-liquid system decreases as temperature increases. The solubility of methane in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the triple point T3 at a certain pressure. We also determined T3 by the three-phase direct coexistence method. The results of both methods agree, and we suggest 295(2) K as the value of T3 for this system. We also analyzed the impact of curvature on the solubility of methane in water. We found that the presence of curvature increases the solubility in both the gas-liquid and hydrate-liquid systems. The change in chemical potential for the formation of hydrate is evaluated along the isobar using two different thermodynamic routes, obtaining good agreement between them. It is shown that the driving force for hydrate nucleation under experimental conditions is higher than that for the formation of pure ice when compared at the same supercooling. We also show that supersaturation (i.e., concentrations above those of the planar interface) increases the driving force for nucleation dramatically. The effect of bubbles can be equivalent to that of an additional supercooling of about 20 K. Having highly supersaturated homogeneous solutions makes possible the spontaneous formation of the hydrate at temperatures as high as 285 K (i.e., 10K below T3). The crucial role of the concentration of methane for hydrate formation is clearly revealed. Nucleation of the hydrate can be either impossible or easy and fast depending on the concentration of methane which seems to play the leading role in the understanding of the kinetics of hydrate formation.

Crystal Prediction via Genetic Algorithms in a Model Chiral System

Chiral crystals and their constituent molecules play a prominent role in theories about the origin of biological homochirality and in drug discovery, design, and stability. Although the prediction and identification of stable chiral crystal structures is crucial for numerous technologies, including separation processes and polymorph selection and control, predictive ability is often complicated by a combination of many-body interactions and molecular complexity and handedness. In this work, we address these challenges by applying genetic algorithms to predict the ground-state crystal lattices formed by a chiral tetramer molecular model, which we have previously shown to exhibit complex fluid-phase behavior. Using this approach, we explore the relative stability and structures of the model's conglomerate and racemic crystals, and present a structural phase diagram for the stable Bravais crystal types in the zero-temperature limit.

Phase Transition between Crystalline Variants of Ordinary Ice

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

Kinetic Phase Diagram for Nucleation and Growth of Competing Crystal Polymorphs in Charged Colloids

We determine the kinetic phase diagram for nucleation and growth of crystal phases in a suspension of charged colloids. Exploiting the seeding approach in extensive simulations, we calculate nucleation barrier heights for face-centered cubic (fcc) and body-centered cubic (bcc) phases for varying screening lengths and supersaturations. We determine for the entire metastable fluid region the crystal polymorph with the lowest nucleation barrier, and find a regime close to the triple point where metastable bcc can form due to a lower nucleation barrier, even though fcc is the stable phase. For higher supersaturation, we find that the difference in barrier heights decreases and we observe a mix of hexagonal close-packed, fcc, and bcc structures in the growth of crystalline seeds as well as in spontaneously formed crystals. Our kinetic phase diagram rationalizes the different crystallization mechanisms observed in previous work.

Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations

Water freezing is the most common liquid-to-crystal phase transition on Earth, however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih, Ic and a stacking mixture of ice Ih/Ic; reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner which contributes to benchmarking the freezing behaviour of two popular water models.

Molecular Mechanism of Organic Crystal Nucleation: A Perspective of Solution Chemistry and Polymorphism

Crystal nucleation determining the formation and assembly pathway of first organic materials is the central science of various scientific disciplines such as chemical, geochemical, biological, and synthetic materials. However, our current understanding of the molecular mechanisms of nucleation remains limited. Over the past decades, the advancements of new experimental and computational techniques have renewed numerous interests in detailed molecular mechanisms of crystal nucleation, especially structure evolution and solution chemistry. These efforts bifurcate into two categories: (modified) classical nucleation theory (CNT) and non-classical nucleation mechanisms. In this review, we briefly introduce the two nucleation mechanisms and summarize current molecular understandings of crystal nucleation that are specifically applied in polymorphic crystallization systems of small organic molecules. Many important aspects of crystal nucleation including molecular association, solvation, aromatic interactions, and hierarchy in intermolecular interactions were examined and discussed for a series of organic molecular systems. The new understandings relating to molecular self-assembly in nucleating systems have suggested more complex multiple nucleation pathways that are associated with the formation and evolution of molecular aggregates in solution.

Freezing point depression of salt aqueous solutions using the Madrid-2019 model

Salt aqueous solutions are relevant in many fields, ranging from biological systems to seawater. Thus, the availability of a force-field that is able to reproduce the thermodynamic and dynamic behavior of salt aqueous solutions would be of great interest. Unfortunately, this has been proven challenging, and most of the existing force-fields fail to reproduce much of their behavior. In particular, the diffusion of water or the salt solubility are often not well reproduced by most of the existing force-fields. Recently, the Madrid-2019 model was proposed, and it was shown that this force-field, which uses the TIP4P/2005 model for water and non-integer charges for the ions, provides a good description of a large number of properties, including the solution densities, viscosities, and the diffusion of water. In this work, we assess the performance of this force-field on the evaluation of the freezing point depression. Although the freezing point depression is a colligative property that at low salt concentrations depends solely on properties of pure water, a good model for the electrolytes is needed to accurately predict the freezing point depression at moderate and high salt concentrations. The coexistence line between ice and several salt aqueous solutions (NaCl, KCl, LiCl, MgCl₂, and Li₂SO₄) up to the eutectic point is estimated from direct coexistence molecular dynamics simulations. Our results show that this force-field reproduces fairly well the experimentally measured freezing point depression with respect to pure water freezing for all the salts and at all the compositions considered.

An investigation of the kinetics and thermodynamics of NaCl nucleation through composite clusters

Having a good understanding of nucleation is critical for the control of many important processes, such as polymorph selection during crystallization. However, a complete picture of the molecular-level mechanisms of nucleation remains elusive. In this work, we take an in-depth look at the NaCl homogeneous nucleation mechanism through thermodynamics. Distinguished from the classical nucleation theory, we calculate the free energy of nucleation as a function of two nucleus size coordinates: crystalline and amorphous cluster sizes. The free energy surface reveals a thermodynamic preference for a nonclassical mechanism of nucleation through a composite cluster, where the crystalline nucleus is surrounded by an amorphous layer. The thickness of the amorphous layer increases with an increase in supersaturation. The computed free energy landscape agrees well with the composite cluster-free energy model, through which phase specific thermodynamic properties are evaluated. As the supersaturation increases, there is a change in stability of the amorphous phase relative to the solution phase, resulting in a change from one-step to two-step mechanism, seen clearly from the free energy profile along the minimum free energy path crossing the transition curve. By obtaining phase-specific diffusion coefficients, we construct the full mesoscopic model and present a clear roadmap for NaCl nucleation.

Signatures of sluggish dynamics and local structural ordering during ice nucleation

We investigate the microscopic pathway of spontaneous crystallization in the ST2 model of water under deeply supercooled conditions via unbiased classical molecular dynamics simulations. After quenching below the liquid–liquid critical point, the ST2 model spontaneously separates into low-density liquid (LDL) and high-density liquid phases, respectively. The LDL phase, which is characterized by lower molecular mobility and enhanced structural order, fosters the formation of a sub-critical ice nucleus that, after a stabilization time, develops into the critical nucleus and grows. Polymorphic selection coincides with the development of the sub-critical nucleus and favors the formation of cubic (Ic) over hexagonal (Ih) ice. We rationalize polymorphic selection in terms of geometric arguments based on differences in the symmetry of second neighbor shells of ice Ic and Ih, which are posited to favor formation of the former. The rapidly growing critical nucleus absorbs both Ic and Ih crystallites dispersed in the liquid phase, a crystal with stacking faults. Our results are consistent with, and expand upon, recent observations of non-classical nucleation pathways in several systems.

On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system

We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.

Homogeneous nucleation of NaCl in supersaturated solutions

The seeding method is an approximate approach to investigate nucleation that combines molecular dynamics simulations with classical nucleation theory. Recently, this technique has been successfully implemented in a broad range of nucleation studies. However, its accuracy is subject to the arbitrary choice of the order parameter threshold used to distinguish liquid-like from solid-like molecules. We revisit here the crystallization of NaCl from a supersaturated brine solution and show that consistency between seeding and rigorous methods, like Forward Flux Sampling (from previous work) or spontaneous crystallization (from this work), is achieved by following a mislabelling criterion to select such threshold (i.e. equaling the fraction of the mislabelled particles in the bulk parent and nucleating phases). This work supports the use of seeding to obtain fast and reasonably accurate nucleation rate estimates and the mislabelling criterion as one giving the relevant cluster size for classical nucleation theory in crystallization studies.

Nucleation rates from small scale atomistic simulations and transition state theory

The evaluation of nucleation rates from molecular dynamics trajectories is hampered by the slow nucleation time scale and impact of finite size effects. Here, we show that accurate nucleation rates can be obtained in a very general fashion relying only on the free energy barrier, transition state theory, and a simple dynamical correction for diffusive recrossing. In this setup, the time scale problem is overcome by using enhanced sampling methods, in casu metadynamics, whereas the impact of finite size effects can be naturally circumvented by reconstructing the free energy surface from an appropriate ensemble. Approximations from classical nucleation theory are avoided. We demonstrate the accuracy of the approach by calculating macroscopic rates of droplet nucleation from argon vapor, spanning 16 orders of magnitude and in excellent agreement with literature results, all from simulations of very small (512 atom) systems.

Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions

Multivalent proteins and nucleic acids can self-assemble into biomolecular condensates that contribute to compartmentalize the cell interior. Computer simulations offer a unique view to elucidate the mechanisms and key intermolecular interactions behind the dynamic formation and dissolution of these condensates. In this work, we present a novel approach to include explicit water and salt in sequence-dependent coarse-grained (CG) models for proteins and RNA, enabling the study of biomolecular condensate formation in a salt-dependent manner. Our framework combines a reparameterized version of the HPS protein force field with the monoatomic mW water model and the mW-ion potential for NaCl. We show how our CG model qualitatively captures the experimental radius of the gyration trend of a subset of intrinsically disordered proteins and reproduces the experimental protein concentration and water percentage of the human fused in sarcoma (FUS) low-complexity-domain droplets at physiological salt concentration. Moreover, we perform seeding simulations as a function of salt concentration for two antagonist systems: the engineered peptide PR₂₅ and poly-uridine/poly-arginine mixtures, finding good agreement with their reported in vitro phase behavior with salt concentration in both cases. Taken together, our work represents a step forward towards extending sequence-dependent CG models to include water and salt, and to consider their key role in biomolecular condensate self-assembly.

The microscopic mechanism of bulk melting of ice

We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.

Underlying Mechanisms of Allopurinol in Eliminating Renal Toxicity Induced by Melamine-Uric Acid Complex Formation: A Computational Study

Using molecular dynamics, we address uric acid (UA) replacement by a model small-molecule inhibitor, allopurinol (AP), from its aggregated cluster in a columnar fashion. Experimentally it has been affirmed that AP is efficient in preventing UA-mediated renal stone formation. However, no study has presented the underlying mechanisms yet. Hence, a theoretical approach is presented for mapping the AP, which binds to melamine (MM) and UA clusters. In AP's presence, the higher-order cluster of UA molecules turns into a lower-order cluster, which "drags" fewer MM to them. Consequently, the MM-UA composite structure gets reduced. It is worth noting that UA-AP and AP-MM hydrogen-bonding interactions often play an essential role in reducing the UA-MM cluster size. Interestingly, an AP around UA makes a pillar-like structure, confirmed by defining the point-plane distribution function. The decomposition of the preferential interaction by Kirkwood-Buff integral into different angles like 0°-30°, 30°-60°, and 60°-90° firmly establishes the phenomenon mentioned above. However, the structural order for such π-stacking interactions between AP and UA molecules is not hierarchical but rather more spontaneous. The driving force behind UA-AP-MM composite formation is the favorable complexation energy that can be inferred by computing pairwise binding free energies for all possible combinations. Performing enhanced sampling and quantum calculations further confirms the evidence for UA degradation.

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details

The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model-let alone to actually understand-be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavor almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects, such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

Universal Nucleation Behavior of Sheared Systems

Using molecular simulations and a modified classical nucleation theory, we study the nucleation, under flow, of a variety of liquids: different water models, Lennard-Jones, and hard sphere colloids. Our approach enables us to analyze a wide range of shear rates inaccessible to brute-force simulations. Our results reveal that the variation of the nucleation rate with shear is universal. A simplified version of the theory successfully captures the nonmonotonic temperature dependence of the nucleation behavior, which is shown to originate from the violation of the Stokes-Einstein relation.

Low Interfacial Free Energy Describes the Bulk Ordering Transition in Colloidal Cubes

Many hard faceted nanoparticles are known to undergo disorder-to-order phase transitions following a classical nucleation and growth mechanism. In a previous study [J. Phys. Chem. B 2018, 122, 9264-9273], it was shown that hard cubes undergo a nonclassical phase transition with a bulk character instead of originating from consolidated nuclei. Significantly, an unusually high fraction of ordered particles was observed in the metastable basin of the disordered phase, even for very low degrees of supersaturation. This work aims to substantiate the conjecture that these unique properties originate from a comparatively low interfacial free energy between the disordered and ordered phases for hard cubes relative to other hard particle systems. Using the cleaving wall method to directly measure the interfacial free energy for cubes, it is found that its values are indeed small; e.g., at phase coexistence conditions, it is only one-fifth that for hard spheres. A theoretical nucleation model is used to explore the broader implications of low interfacial tension values and how this could result in a bulk ordering mechanism.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

Liquid Water and Interfacial, Cubic, and Hexagonal Ice Classification through Eclipsed and Staggered Conformation Template Matching

We propose a novel method based on template matching for the recognition of liquid water, cubic ice (ice I_c), hexagonal ice (ice I_h), clathrate hydrates, and different interfacial structures in atomistic and coarse-grained simulations of water and ice. The two template matrices represent staggered and eclipsed conformations, which are the building blocks of hexagonal and cubic ice and clathrate crystals. The algorithm is rotationally invariant and highly robust against imperfections in the ice structure, and its sensitivity for recognizing ice-like structures can be tuned for different applications. Unlike most other algorithms, it can discriminate between cubic, hexagonal, clathrate, mixed, and other interfacial ice types and is therefore well suited to study complex systems and heterogeneous ice nucleation.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation ratesITin the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the sizen_cand geometrical configuration of critical nuclei as well as their liquid-solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling ofTm=0.42Tmcal, the average size of critical nuclei is demonstrated to benc̄≈26, but most of which are non-spherical lamellae. Also, their liquid-solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments inITindicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

An Artificial Neural Network Reveals the Nucleation Mechanism of a Binary Colloidal AB13 Crystal

Colloidal suspensions of two species have the ability to form binary crystals under certain conditions. The hunt for these functional materials and the countless investigations on their formation process are justified by the plethora of synergetic and collective properties these binary superlattices show. Among the many crystal structures observed over the past decades, the highly exotic colloidal icosahedral AB₁₃ crystal was predicted to be stable in binary hard-sphere mixtures nearly 30 years ago, yet the kinetic pathway of how homogeneous nucleation occurs in this system is still unknown. Here we investigate binary nucleation of the AB₁₃ crystal from a binary fluid phase of nearly hard spheres. We calculate the nucleation barrier and nucleation rate as a function of supersaturation and draw a comparison with nucleation of single-component and other binary crystals. To follow the nucleation process, we employ a neural network to identify the AB₁₃ phase from the binary fluid phase and the competing fcc crystal with single-particle resolution and significant accuracy in the case of bulk phases. We show that AB₁₃ crystal nucleation proceeds via a coassembly process where large spheres and icosahedral small-sphere clusters simultaneously attach to the nucleus. Our results lend strong support for a classical pathway that is well-described by classical nucleation theory, even though the binary fluid phase is highly structured and exhibits local regions of high bond orientational order.