Nucleation in aqueous NaCl solutions shifts from 1-step to 2-step mechanism on crossing the spinodal

Crumbling crystals: on the dissolution mechanism of NaCl in water

Dissolution of ionic salts in water is ubiquitous, particularly for NaCl. However, an atomistic scale understanding of the process remains elusive. Simulations lend themselves conveniently to studying dissolution since they provide the spatio-temporal resolution that can be difficult to obtain experimentally. Nevertheless, the complexity of various inter- and intra-molecular interactions require careful treatment and long time scale simulations, both of which are typically hindered by computational expense. Here, we use advances in machine learning potential methodology to resolve at an ab initio level of theory the dissolution mechanism of NaCl in water. The picture that emerges is that of a steady ion-wise unwrapping of the crystal preceding its rapid disintegration, reminiscent of crumbling. The onset of crumbling can be explained by a strong increase in the ratio of the surface area to volume of the crystal. Overall, dissolution comprises a series of highly dynamical microscopic sub-processes, resulting in an inherently stochastic mechanism. These atomistic level insights contribute to the general understanding of dissolution mechanisms in other crystals, and the methodology is primed for more complex systems of recent interest such as water/salt interfaces under flow and salt crystals under confinement.

Atomic scale insights into NaCl nucleation in nanoconfined environments

In this work we examine the nucleation from NaCl aqueous solutions within nano-confined environments, employing enhanced sampling molecular dynamics simulations integrated with machine learning-derived reaction coordinates. Through our simulations, we successfully induce phase transitions between solid, liquid, and a hydrated phase, typically observed at lower temperatures in bulk environments. Interestingly, while generally speaking nano-confinement serves to stabilize the solid phase and elevate melting points, there are subtle variations in the thermodynamics of competing phases with the precise extent of confinement. Our simulations explain these findings by underscoring the significant role of water, alongside ion aggregation and subtle, anisotropic dielectric behavior, in driving nucleation within nano-confined environments. This report thus provides a framework for sampling, analyzing and understanding nucleation processes under nano-confinement.

Stochastic computer experiments of the thermodynamic irreversibility of bulk nanobubbles in supersaturated and weak gas-liquid solutions

Spontaneous gas-bubble nucleation in weak gas-liquid solutions has been a challenging topic in theory, experimentation, and computer simulations. In analogy with recent advances in crystallization and droplet formation studies, the diffusive-shielding stabilization and thermodynamic irreversibility of bulk nanobubble (bNB) mechanisms are revisited and deployed to characterize nucleation processes in a stochastic framework of computer experiments using the large-scale atomic/molecular massively parallel simulator code. Theoretical bases, assumptions, and limitations underlying the irreversibility hypothesis of bNBs, and their computational counterparts, are extensively described and illustrated. In essence, it is established that the irreversibility hypothesis can be numerically investigated by converging the system volume (due to the finiteness of interatomic forces) and the initial dissolved-gas concentration in the solution (due to the single-bNB limitation). Helium nucleation in liquid Pb17Li alloy is selected as a representative case study, where it exhibits typical characteristics of noble-gas/liquid-metal systems. The proposed framework lays down the bases on which the stability of gas-bNBs in weak and supersaturated gas-liquid solutions can be inferred and explained from a novel perspective. In essence, it stochastically marches toward a unique irreversible state along out-of-equilibrium nucleation/growth trajectories. Moreover, it does not attempt to characterize the interface or any interface-related properties, neither theoretically nor computationally. It was concluded that bNBs of a few tens of He-atoms are irreversible when dissolved-He concentrations in the weak gas-liquid solution are at least ∼50 and ∼105 mol m-3 at 600 and 1000 K (and ∼80 MPa), respectively, whereas classical molecular dynamics -estimated solubilities are at least two orders of magnitude smaller.

Convergence of dissolving and melting at the nanoscale

Phase transitions of water and its mixtures are of fundamental importance in physical chemistry, the pharmaceutical industry, materials sciences, and atmospheric sciences. However, current understanding remains elusive to explain relevant observations, especially at the nanoscale. Here, by using molecular dynamics simulations, we investigate the dissolution of sodium chloride (NaCl) nanocrystals with volume-equivalent diameters from 0.51 to 1.75 nm. Our results show that the dissolution of NaCl in aqueous nanodroplets show a strong size dependence, and its solubility can be predicted by the Ostwald-Freundlich equation and Gibbs-Duhem equation after considering a size-dependent solid-liquid surface tension. We find that the structure of dissolved ions in the saturated aqueous nanodropplet resembles the structure of a molten NaCl nanoparticle. With decreasing nanodroplet size, this similarity grows and the average potential energy of NaCl in solution, the molten phase and the crystal phase converges.

Properties of aqueous electrolyte solutions at carbon electrodes: effects of concentration and surface charge on solution structure, ion clustering and thermodynamics in the electric double layer

Surfaces are able to control physical-chemical processes in multi-component solution systems and, as such, find application in a wide range of technological devices. Understanding the structure, dynamics and thermodynamics of non-ideal solutions at surfaces, however, is particularly challenging. Here, we use Constant Chemical Potential Molecular Dynamics (CμMD) simulations to gain insight into aqueous NaCl solutions in contact with graphite surfaces at high concentrations and under the effect of applied surface charges: conditions where mean-field theories describing interfaces cannot (typically) be reliably applied. We discover an asymmetric effect of surface charge on the electric double layer structure and resulting thermodynamic properties, which can be explained by considering the affinity of the surface for cations and anions and the cooperative adsorption of ions that occurs at higher concentrations. We characterise how the sign of the surface charge affects ion densities and water structure in the double layer and how the capacitance of the interface-a function of the electric potential drop across the double layer-is largely insensitive to the bulk solution concentration. Notably, we find that negatively charged graphite surfaces induce an increase in the size and concentration of extended liquid-like ion clusters confined to the double layer. Finally, we discuss how concentration and surface charge affect the activity coefficients of ions and water at the interface, demonstrating how electric fields in this region should be explicitly considered when characterising the thermodynamics of both solute and solvent at the solid/liquid interface.

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.

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.

Mechanism of Nucleation Pathway Selection in Binary Lennard-Jones Solution: A Combined Study of Molecular Dynamics Simulation and Free Energy Analysis

The nucleation process, which is the initial step in particle synthesis, determines the properties of the resultant particles. Although recent studies have observed various nucleation pathways, the physical factors that determine these pathways have not been fully elucidated. Herein, we conducted molecular dynamics simulations in a binary Lennard-Jones system as a model solution and found that the nucleation pathway can be classified into four types depending on microscopic interactions. The key parameters are (1) the strength of the solute-solute interaction and (2) the difference between the strengths of the like-pair and unlike-pair interactions. The increment of the former alters the nucleation mechanism from a two-step to a one-step pathway, whereas that of the latter causes quick assembly of solutes. Moreover, we developed a thermodynamic model based on the formation of core-shell nuclei to calculate the free energy landscapes. Our model successfully described the pathway observed in the simulations and demonstrated that the two parameters, (1) and (2), define the degree of supercooling and supersaturation, respectively. Thus, our model interpreted the microscopic insights from a macroscopic point of view. Because the only inputs required for our model are the interaction parameters, our model can a priori predict the nucleation pathway.

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).

A variational approach to assess reaction coordinates for two-step crystallization

Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavor, determining nucleation mechanisms and rates for phase separation requires an appropriately defined reaction coordinate to describe the transformation of an out-of-equilibrium parent phase for which myriad options are available to the simulator. In this article, we describe the application of the variational approach to Markov processes to quantify the suitability of reaction coordinates to study crystallization from supersaturated colloid suspensions. Our analysis indicates that collective variables (CVs) that correlate with the number of particles in the condensed phase, the system potential energy, and approximate configurational entropy often feature as the most appropriate order parameters to quantitatively describe the crystallization process. We apply time-lagged independent component analysis to reduce high-dimensional reaction coordinates constructed from these CVs to build Markov State Models (MSMs), which indicate that two barriers separate a supersaturated fluid phase from crystals in the simulated environment. The MSMs provide consistent estimates for crystal nucleation rates, regardless of the dimensionality of the order parameter space adopted; however, the two-step mechanism is only consistently evident from spectral clustering of the MSMs in higher dimensions. As the method is general and easily transferable, the variational approach we adopt could provide a useful framework to study controls for crystal nucleation.

Nucleation Rate Theory for Coordination Number: Elucidating Water-Mediated Formation of a Zigzag Na2SO4 Morphology

Predicting and controlling nanostructure formation during nucleation can pave the way to synthesizing novel energy materials via crystallization. However, such control over nucleation and crystallization remains challenging due to an inadequate understanding of critical factors that govern evolving atomistic structures and dynamics. Herein, we utilize coordination number as a reaction coordinate and rate theory to investigate how sodium sulfate, commonly known as a phase-change energy material, nucleates in a supersaturated aqueous solution. In conjunction with ab initio and force field-based molecular dynamics simulation, the rate theoretical analysis reveals that sodium sulfate from an initially dissolved metastable state transits to a heterogeneous mixture of prenucleated clusters and finally to a large cylindrical zigzag morphology. Measurements of Raman spectra and their ab initio modeling confirm that this nucleated morphology contains a few waters for every sulfate. Rate processes such as solvent exchange and desolvation exhibit high sensitivity to the evolving prenucleation/nucleation structures, providing a means to distinguish between critical nucleation precursors. Desolvation and forming the first-shell interionic coordination structure via monomer-by-monomer addition around sulfates are found to explain the formation of large nuclei. Thus, a detailed understanding of the step-by-step structure formation across scales has been achieved. This can be leveraged to predict nucleation-related structures and dynamics and potentially control the synthesis of novel phase-change materials for energy applications.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of r _A/r _B = 0.8 to r _A/r _B = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Quantifying Energetic and Entropic Pathways in Molecular Systems

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

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.

Activity Coefficients and Solubilities of NaCl in Water-Methanol Solutions from Molecular Dynamics Simulations

We obtain activity coefficients and solubilities of NaCl in water-methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung-Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz-Berthelot combining rules were adopted for the unlike-pair interactions of Na⁺, Cl^-, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na⁺ and Cl^- from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.

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.

Fluorescence of KCl Aqueous Solution: A Possible Spectroscopic Signature of Nucleation

Ion pairing in water solutions alters both the water hydrogen-bond network and ion solvation, modifying the dynamics and properties of electrolyte water solutions. Here, we report an anomalous intrinsic fluorescence of KCl aqueous solution at room temperature and show that its intensity increases with the salt concentration. From the ab initio density functional theory (DFT) and time-dependent DFT modeling, we propose that the fluorescence emission could originate from the stiffening of the hydrogen bond network in the hydration shell of solvated ion-pairs that suppresses the fast nonradiative decay and allows the slower radiative channel to become a possible decay pathway. Because computations suggest that the fluorophores are the local ion-water structures present in the prenucleation phase, this band could be the signature of the incoming salt precipitation.

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.

Temperature and Pressure Dependence of Salt-Brine Dihedral Angles in the Subsurface

Elevated temperature and pressure in the earth's subsurface alters the permeability of salt formations, due to changing properties of the salt-brine interface. Molecular dynamics (MD) simulations are used to investigate the mechanisms of temperature and pressure dependence of liquid-solid interfacial tensions of NaCl, KCl, and NaCl-KCl brines in contact with (100) salt surfaces. Salt-brine dihedral angles vary between 55 and 76° across the temperature (300-450 K) and pressure range (0-150 MPa) evaluated. Temperature-dependent brine composition results in elevated dihedral angles of 65-80°, which falls above the reported salt percolation threshold of 60°. Mixed NaCl-KCl brine compositions increased this effect. Elevated temperatures excluded dissolved Na⁺ ions from the interface, causing the strong temperature dependence of the liquid-solid interfacial tension and the resulting dihedral angle. Therefore, at higher temperature, pressure, and brine concentrations Na-Cl systems may underpredict the dihedral angle. Higher dihedral angles in more realistic mixed brine systems maintain low permeability of salt formations due to changes in the structure and energetics of the salt-brine interface.

Electrochemistry, ion adsorption and dynamics in the double layer: a study of NaCl(aq) on graphite

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

CμMD reveals multi-layer electrolyte screening in the double layer beyond 0.6 M, which affects ion activities, speciation and mobility; asymmetric charge screening explains concentration dependent changes to electrochemical properties.

Free energy surface of two-step nucleation

We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] by comparing the predictions of the theory to numerical results for the FES recently reported from Monte Carlo simulations of TSN in a simple lattice system [James et al., J. Chem. Phys. 150, 074501 (2019)]. No adjustable parameters are used to make this comparison. That is, all the parameters of the theory are evaluated directly for the model system, yielding a predicted FES, which we then compare to the FES obtained from simulations. We find that the theoretical FES successfully predicts the numerically evaluated FES over a range of thermodynamic conditions that spans distinct regimes of behavior associated with TSN. All the qualitative features of the FES are captured by the theory, and the quantitative comparison is also very good. Our results demonstrate that Iwamatsu's extension of classical nucleation theory provides an excellent framework for understanding the thermodynamics of TSN.

Microscopic Kinetics Pathway of Salt Crystallization in Graphene Nanocapillaries

The fundamental understanding of crystallization, in terms of microscopic kinetic and thermodynamic details, remains a key challenge in the physical sciences. Here, by using in situ graphene liquid cell transmission electron microscopy, we reveal the atomistic mechanism of NaCl crystallization from solutions confined within graphene cells. We find that rock salt NaCl forms with a peculiar hexagonal morphology. We also see the emergence of a transitory graphitelike phase, which may act as an intermediate in a two-step pathway. With the aid of density functional theory calculations, we propose that these observations result from a delicate balance between the substrate-solute interaction and thermodynamics under confinement. Our results highlight the impact of confinement on both the kinetics and thermodynamics of crystallization, offering new insights into heterogeneous crystallization theory and a potential avenue for materials design.

NaCl aggregation in water at elevated temperatures and pressures: Comparison of classical force fields

The properties of water vary dramatically with temperature and density. This can be exploited to control its effectiveness as a solvent. Thus, supercritical water is of keen interest as solvent in many extraction processes. The low solubility of salts in lower density supercritical water has even been suggested as a means of desalination. The high temperatures and pressures required to reach supercritical conditions can present experimental challenges during collection of required physical property and phase equilibria data, especially in salt-containing systems. Molecular simulations have the potential to be a valuable tool for examining the behavior of solvated ions at these high temperatures and pressures. However, the accuracy of classical force fields under these conditions is unclear. We have, therefore, undertaken a parametric study of NaCl in water, comparing several salt and water models at 200 bar-600 bar and 450 K-750 K for a range of salt concentrations. We report a comparison of structural properties including ion aggregation, hydrogen bonding, density, and static dielectric constants. All of the force fields qualitatively reproduce the trends in the liquid phase density. An increase in ion aggregation with decreasing density holds true for all of the force fields. The propensity to aggregate is primarily determined by the salt force field rather than the water force field. This coincides with a decrease in the water static dielectric constant and reduced charge screening. While a decrease in the static dielectric constant with increasing NaCl concentration is consistent across all model combinations, the salt force fields that exhibit more ionic aggregation yield a slightly smaller dielectric decrement.

Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase

Colloidal particles have been extensively used to comprehend the main principles governing liquid-crystal nucleation. Multiple mechanisms and frameworks have been proposed, through either experiments or computational approaches, to rationalise the ubiquitous formation of colloidal crystals. In this work, we elucidate the nucleation scenario behind the crystallization of oppositely charged colloids. By performing molecular dynamics simulations of colloidal electrolytes in combination with the Seeding technique, we evaluate the fundamental factors, such as the nucleation rate, free energy barrier, surface tension and kinetic pre-factor, that determine the liquid-to-solid transition of several crystalline polymorphs. Our results show that at a high packing fraction, there is a cross-over between the nucleation of the CsCl structure and that of a substitutionally disordered fcc phase, despite the CuAu crystal being the most stable phase. We demonstrate that the crucial factor in determining which phase nucleates the fastest is the free energy cost of the cluster formation rather than their kinetic ability to grow from the liquid. While at a low packing fraction, the stable phase, CsCl, is the one that nucleates and subsequently grows, we show how at moderate and high packing fractions, a disordered fcc phase subsequently grows regardless of the nature of the nucleating phase, termed parasitic crystallization. Taken together, our results provide a panoramic perspective of the complex nucleation scenario of oppositely charged colloids at moderate temperature and rationalise the different thermodynamic and kinetic aspects behind it.

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...

Hydration breaking and chemical ordering in a levitated NaCl solution droplet beyond the metastable zone width limit: evidence for the early stage of two-step nucleation

For over two decades, NaCl nucleation from a supersaturated aqueous solution has been predicted to occur via a two-step nucleation (TSN) mechanism, i.e., two sequential events, the formation of locally dense liquid regions followed by structural ordering. However, the formation of dense liquid regions in the very early stage of TSN has never been experimentally observed. By using a state-of-the-art technique, a combination of electrostatic levitation (ESL) and in situ synchrotron X-ray and Raman scatterings, we find experimental evidence that indicates the formation of dense liquid regions in NaCl bulk solution at an unprecedentedly high level of supersaturation (S = 2.31). As supersaturation increases, evolution of ion clusters leads to chemical ordering, but no topological ordering, which is a precursor for forming the dense disordered regions of ion clusters at the early stage of TSN. Moreover, as the ion clusters proceed to evolve under highly supersaturated conditions, we observe the breakage of the water hydration structure indicating the stability limit of the dense liquid regions, and thus leading to nucleation. The evolution of solute clusters and breakage of hydration in highly supersaturated NaCl bulk solution will provide new insights into the detailed mechanism of TSN for many other aqueous solutions.

Using Excimeric Fluorescence to Study How the Cooling Rate Determines the Behavior of Naphthalenes in Freeze-Concentrated Solutions: Vitrification and Crystallization

We utilized fluorescence spectroscopy to learn about the molecular arrangement of naphthalene (Np) and 1-methylnaphthalene (MeNp) in frozen aqueous solutions. The freezing induces pronounced compound aggregation in the freeze-concentrated solution (FCS) in between the ice grains. The fluorescence spectroscopy revealed prevalent formation of a vitrified solution and minor crystallization of aromatic compounds. The FCS is shown as a specific environment, differing significantly from not only the pure compounds but also the ice surfaces. The results indicate marked disparity between the behavior of the Np and the MeNp; the cooling rate has a major impact on the former but not on the latter. The spectrum of the Np solution frozen at a faster cooling rate (ca 20 K/min) exhibited a temperature-dependent spectral behavior, whereas the spectrum of the solution frozen at a slower rate (ca 2 K/min) did not alter before melting. We interpret the observation through considering the varied composition of the FCS: Fast freezing leads to a higher water content expressed by the plasticizing effect, allowing molecular rearrangement, while slow cooling produces a more concentrated and drier environment. The experiments were conceived as generalizable for environmentally relevant pollutants and human-made freezing.

Experimental observation of nanophase segregation in aqueous salt solutions around the predicted liquid-liquid transition in water

The liquid-liquid transition in supercooled liquid water, predicted to occur around 220 K, is controversial due to the difficulty of studying it caused by competition from ice crystallization (the so-called "no man's land"). In aqueous solutions, it has been predicted to give rise to phase separation on a nanometer scale between a solute-rich high-density phase and a water-rich low-density phase. Here we report direct experimental evidence for the formation of a nanosegregated phase in eutectic aqueous solutions of LiCl and LiSCN where the presence of crystalline water can be experimentally excluded. Femtosecond infrared and Raman spectroscopies are used to determine the temperature-dependent structuring of water, the solvation of the SCN^- anion, and the size of the phase segregated domains.

Homogeneous Nucleation Mechanism of NaCl in Aqueous Solutions

In this study, molecular dynamic simulations are employed to investigate the homogeneous nucleation mechanism of NaCl crystal in solutions. According to the simulations, the dissolved behaviors of NaCl in water are dependent on ion concentrations. With increasing NaCl concentrations, the dissolved Na+ and Cl- ions tend to be aggregated in solutions. In combination with our recent studies, the aggregate of dissolved solutes is mainly ascribed to the hydrophobic interactions. Different from the two-step mechanism, no barrier is needed to overcome the formation of the aggregate. In comparison with the classical nucleation theory (CNT), because of the formation of solute aggregate, this lowers the barrier height of nucleation and affects the nucleation mechanism of NaCl crystal in water.

Recent experimental explorations of non-classical nucleation

This work provides a clearer picture for non-classical nucleation by revealing the presence of various intermediates using advanced characterization techniques.

Entropic colloidal crystallization pathways via fluid-fluid transitions and multidimensional prenucleation motifs

Complex crystallization pathways are common in protein crystallization, tetrahedrally coordinated systems, and biomineralization, where single or multiple precursors temporarily appear before the formation of the crystal. The emergence of precursors is often explained by a unique property of the system, such as short-range attraction, directional bonding, or ion association. But, structural characteristics of the prenucleation phases found in multistep crystallization remain unclear, and models are needed for testing and expanding the understanding of fluid-to-solid ordering pathways. Here, we report 3 instances of 2-step crystallization of hard-particle fluids. Crystallization in these systems proceeds via a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. The density and diffusivity change across the fluid-fluid phase transition increases with motif dimension. We observe crystal nucleation to be catalyzed by the interface between the 2 fluid phases. The crystals that form are complex, including, notably, a crystal with 432 particles in the cubic unit cell. Our results establish the existence of complex crystallization pathways in entropic systems and reveal prenucleation motifs of various dimensions.

Ice Nucleation of Confined Monolayer Water Conforms to Classical Nucleation Theory

We confirmed that monolayer water confined by parallel graphene sheets spontaneously crystallizes from a structurally and dynamically heterogeneous liquid phase under moderate supercooling via direct molecular dynamics simulation. Square-lattice-like geometric order is observed at the early stage of nucleation and is preserved during the entire nucleus growth process. The diffusion coefficient and free energy profile in the cluster space extracted from a Bayesian trajectory analysis agree well with the classical nucleation theory (CNT) prediction and yield thermodynamic quantities exhibiting linear temperature dependence. The effectiveness of maximum cluster size as the descriptor of ice nucleation dynamics in the CNT framework can be attributed to the dynamical time scale decoupling and strong structural pattern dependence of density fluctuation in the liquid phase.