Homogeneous nucleation of NaCl in supersaturated solutions

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

CNT effective interfacial energy and pre-exponential kinetic factor from measured NaCl crystal nucleation time distributions in contracting microdroplets

Nucleation, the birth of a stable cluster from a disorder, is inherently stochastic. Yet up to date, there are no quantitative studies on NaCl nucleation that accounts for its stochastic nature. Here, we report the first stochastic treatment of NaCl-water nucleation kinetics. Using a recently developed microfluidic system and evaporation model, our measured interfacial energies extracted from a modified Poisson distribution of nucleation time show an excellent agreement with theoretical predictions. Furthermore, analysis of nucleation parameters in 0.5, 1.5, and 5.5 pl microdroplets reveals an interesting interplay between confinement effects and shifting of nucleation mechanisms. Overall, our findings highlight the need to treat nucleation stochastically rather than deterministically to bridge the gap between theory and experiment.

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.

A Tale of Two Foulants: The Coupling of Organic Fouling and Mineral Scaling in Membrane Desalination

Membrane desalination that enables the harvesting of purified water from unconventional sources such as seawater, brackish groundwater, and wastewater has become indispensable to ensure sustainable freshwater supply in the context of a changing climate. However, the efficiency of membrane desalination is greatly constrained by organic fouling and mineral scaling. Although extensive studies have focused on understanding membrane fouling or scaling separately, organic foulants commonly coexist with inorganic scalants in the feedwaters of membrane desalination. Compared to individual fouling or scaling, combined fouling and scaling often exhibits different behaviors and is governed by foulant-scalant interactions, resembling more complex but practical scenarios than using feedwaters containing only organic foulants or inorganic scalants. In this critical review, we first summarize the performance of membrane desalination under combined fouling and scaling, involving mineral scales formed via both crystallization and polymerization. We then provide the state-of-the-art knowledge and characterization techniques pertaining to the molecular interactions between organic foulants and inorganic scalants, which alter the kinetics and thermodynamics of mineral nucleation as well as the deposition of mineral scales onto membrane surfaces. We further review the current efforts of mitigating combined fouling and scaling via membrane materials development and pretreatment. Finally, we provide prospects for future research needs that guide the design of more effective control strategies for combined fouling and scaling to improve the efficiency and resilience of membrane desalination for the treatment of feedwaters with complex compositions.

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.

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).

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.

Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles

Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.

Solvation structures of calcium and magnesium ions in water with the presence of hydroxide: a study by deep potential molecular dynamics

The solvation structures of calcium (Ca²⁺) and magnesium (Mg²⁺) ions with the presence of hydroxide (OH^-) ion in water are essential for understanding their roles in biological and chemical processes but have not been fully explored. Ab initio molecular dynamics (AIMD) is an important tool to address this issue, but two challenges exist. First, an accurate description of OH^- from AIMD needs an appropriate exchange-correlation functional. Second, a long trajectory is needed to reach an equilibrium state for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in aqueous solutions. Herein, we adopt a deep potential molecular dynamics (DPMD) method to simulate 1 ns trajectories for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in water; the DPMD method provides efficient machine-learning-based models that have the accuracy of the SCAN exchange-correlation functional within the framework of density functional theory. The solvation structures of the cations and the OH^- in terms of three different species have been systematically investigated. On the one hand, we find that OH^- have more significant effects on the solvation structure of Ca²⁺ than that of Mg²⁺. We observe that the OH^- substantially affects the orientation angles of water molecules surrounding the cation. Through the time correlation functions, we conclude that the water molecules in the first solvation shell of Ca²⁺ change their preferred orientation faster than those of Mg²⁺. On the other hand, with the presence of the cation in the first solvation shell of OH^-, we find that the hydrogen bonds of OH^- are severely altered, and the adjacent water molecules of OH^- are squeezed. The two cations have substantially different effects on the solvation structure of OH^-. Our work provides new insight into the solvation structures of Ca²⁺ and Mg²⁺ in water with the presence of OH^-.

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.

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

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.

Maximum in density of electrolyte solutions: Learning about ion-water interactions and testing the Madrid-2019 force field

In this work, we studied the effect of Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ chlorides and sulfates on the temperature of maximum density (TMD) of aqueous solutions at room pressure. Experiments at 1 molal salt concentration were carried out to determine the TMD of these solutions. We also performed molecular dynamics simulations to estimate the TMD at 1 and 2 m with the Madrid-2019 force field, which uses the TIP4P/2005 water model and scaled charges for the ions, finding an excellent agreement between experiment and simulation. All the salts studied in this work shift the TMD of the solution to lower temperatures and flatten the density vs temperature curves (when compared to pure water) with increasing salt concentration. The shift in the TMD depends strongly on the nature of the electrolyte. In order to explore this dependence, we have evaluated the contribution of each ion to the shift in the TMD concluding that Na⁺, Ca²⁺, and SO₄ ^2- seem to induce the largest changes among the studied ions. The volume of the system has been analyzed for salts with the same anion and different cations. These curves provide insight into the effect of different ions upon the structure of water. We claim that the TMD of electrolyte solutions entails interesting physics regarding ion-water and water-water interactions and should, therefore, be considered as a test property when developing force fields for electrolytes. This matter has been rather unnoticed for almost a century now and we believe it is time to revisit it.

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.

Multiple Pathways in NaCl Homogeneous Crystal Nucleation

NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism where the growth in the size and crystalline order of the emerging nuclei...