Nucleation of NaCl from Aqueous Solution: Critical Sizes, Ion-Attachment Kinetics, and Rates

Interfacial and temperature behaviors of concentrated NaCl solutions bound to hydrophilic and hydrophobic nanosilicas under confined space and cryoscopic effects

HYPOTHESIS

The aqueous solutions behaviors could change under confined space effects (CSE). The nature of pore surface could affect the interfacial phenomena including CSE and cryoscopic effects (CE) in addition to decreased solvent activity under CSE.

EXPERIMENTS

Hydrophobic (AM1) and hydrophilic (A-300) nanosilicas were used to analyze CSE/CE on bound water and NaCl/water using microscopy, adsorption, XRD, infrared and NMR spectroscopies, thermogravimetry, rheometry, and quantum chemistry.

FINDINGS

Water and salt solutions bound to nanosilicas include weakly (frozen at 260 K < T < 273 K) and strongly (frozen at T < 260 K) bound waters, and weakly (chemical shift δH = 0.5-2 ppm) and strongly (δH = 4-6 ppm) associated waters. For bound water/NaCl, there is frozen water with melting delay at 273 K < T < 287 K (metastable water, MSW). MSW appearance is explained by release of water trapped in condensed NaCl dissolved at T > 273 K upon increasing amounts of liquid water with temperature. The difference in the AM1 and A-300 effects onto bound water is due to AM1 Si(CH3)2 'umbrellas' enhancing bound water clusterization. Structural and morphological features of AM1 and A-300 differently affect: (i) NaCl crystallite size distributions; (ii) melting/crystallization temperatures of NaCl; (iii) viscosity and torque vs. shear rate; (iv) temperature and interfacial behaviors of water alone and NaCl solutions; and (v) CSE/CE and effects of dispersion media. Obtained results are of interest from theoretical and practical points of view since various nanosilicas are used as components of composites containing water and NaCl or other salts in various applications in medicine, agriculture, etc.

Developing a Vial-Scale Methodology for the Measurement of Nucleation Kinetics Using Evaporative Crystallization: A Case Study with Sodium Chloride

Understanding nucleation kinetics is vital for designing crystallization processes, yet traditional measurement methods based on cooling are unsuitable for compounds with temperature-independent solubility. This study introduces an experimental procedure to measure the nucleation kinetics based on evaporative crystallization and applies it to sodium chloride (NaCl) in water. By systematically varying the experimental conditions such as temperature and evaporation gas flow rate, we obtained a comprehensive data set for the nucleation of NaCl crystals that allowed estimating kinetic parameters using a rate expression derived from classical nucleation theory (CNT). This work demonstrates the robustness of evaporation as a method for measuring the nucleation kinetics that is applicable regardless of how the solubility of a compound depends on the temperature.

Low-temperature nucleation rate calculations using the N-Fold way

We present a numerical study to determine nucleation rates for magnetization reversal within the Ising model (lattice gas model) in the low-temperature regime, a domain less explored in previous research. To achieve this, we implemented the N-Fold way algorithm, a well-established method for low-temperature simulations, alongside a novel, highly efficient cluster identification algorithm. Our method can access nucleation rates up to 50 orders of magnitude lower than previously reported results. We examine three cases: homogeneous pure system, system with static impurities, and system with mobile impurities, where impurities are defined as sites with zero interactions with neighboring spins (the spin value of impurities is set to 0). Classical nucleation theory holds across the entire temperature range studied in the paper, for both the homogeneous system and the static impurity case. However, in the case of mobile impurities, the umbrella sampling technique appears ineffective at low mobility values. These findings provide valuable insights into nucleation phenomena at low temperatures, contributing to theoretical and experimental understanding.

Fully Atomistic Molecular Dynamics Simulation of Ice Nucleation Near an Antifreeze Protein

Heterogeneous ice nucleation is a widespread phenomenon in nature. Despite extensive research on ice nucleation near biological antifreeze proteins, a probe for ice nucleation and growth processes at the atomic level is still lacking. Herein, we present simulation evidence of the heterogeneous ice nucleation process on the ice-binding surface (IBS) of the Tenebrio molitor antifreeze protein (TmAFP). Our all-atomistic molecular dynamics simulations reveal detailed steps toward precritical nucleus formation from one-dimensional (1D) channel water to a 2D ice nanolayer and, finally, a 3D ice nucleus. Compared with homogeneous ice nucleation under the same supercooling conditions, the IBS of TmAFP can markedly reduce the critical size of the ice embryo and lower the nucleation free energy barrier, thereby favoring ice nucleation. Additionally, through artificial mutation of selected functional groups on the IBS, we gain deeper insights into how the specific functional groups of the IBS affect ice nucleation. We highlight that the carbonyl groups in the backbone play a crucial role by providing fixed locations for channel water. This function is essential for ensuring alignment between the 2D ice nanolayer and the ice lattice structure.

Solution Thermodynamics of l-Glutamic Acid Polymorphs from Finite-Sized Molecular Dynamics Simulations

Efficiently obtaining atomic-scale thermodynamic parameters characterizing crystallization from solution is key to developing the modeling strategies needed in the quest for digital design strategies for industrial crystallization processes. Based on the thermodynamics of crystal nucleation in confined solutions, we develop a simulation framework to efficiently estimate the solubility and surface tension of organic crystals in solution from a few unbiased molecular dynamics simulations at a reference temperature. We then show that such a result can be extended with minimal computational overhead to capture the solubility curve. This enables an efficient and self-consistent estimate of the solubility and limit of solution stability associated with crystal nucleation in molecular systems from equilibrium molecular dynamics without the need for sophisticated free energy calculations. We apply our analysis to investigate the relative thermodynamic stability and aqueous solubility of the α and β polymorphs of l-glutamic acid. Our analysis enables an efficient appraisal of emergent ensemble properties associated with the thermodynamics of nucleation from solutions against experimental data, demonstrating that while the absolute solubility is still far from being quantitatively captured by an off-the-shelf point charge transferable force field, the relative polymorphic stability and solubility obtained from finite temperature simulation are consistent with the experimentally available information on glutamic acid. We foresee the ability to efficiently obtain solubility information from a limited number of computational experiments as a critical component of high-throughput polymorph screenings.

Weather-related changes in the dehydration of respiratory droplets on surfaces bolster bacterial endurance

HYPOTHESIS

The study shows for the first time a fivefold difference in the survivability of the bacterium Pseudomonas Aeruginosa (PA) in a realistic respiratory fluid droplet on fomites undergoing drying at different environmental conditions. For instance, in 2023, the annual average outdoor relative humidity (RH) and temperature in London (UK) is 71 % and 11 °C, whereas in New Delhi (India), it is 45 % and 26 °C, showing that disease spread from fomites could have a demographic dependence. Respiratory fluid droplet ejections containing pathogens on inanimate surfaces are crucial in disease spread, especially in nosocomial settings. However, the interplay between evaporation dynamics, internal fluid flow and precipitation and their collective influence on the distribution and survivability of pathogens at different environmental conditions are less known.

EXPERIMENTS

Shadowgraphy imaging is employed to study evaporation, and optical microscopy imaging is used for precipitation dynamics. Micro-particle image velocimetry (MicroPIV) measurements reveal the internal flow dynamics. Confocal imaging of fluorescently labelled PA elucidates the bacterial distribution within the deposits.

FINDINGS

The study finds that the evaporation rate is drastically impeded during drying at elevated solutal concentrations, particularly at high RH and low temperature conditions. MicroPIV shows reduced internal flow under high RH and low temperature (low evaporation rate) conditions. Evaporation rate influences crystal growth, with delayed efflorescence and extending crystallization times. PA forms denser peripheral arrangements under high evaporation rates and shows a fivefold increase in survivability under low evaporation rates. These findings highlight the critical impact of environmental conditions on pathogen persistence and disease spread from inanimate surfaces.

A perspective view of salt crystallization from solution in porous media: morphology, mechanism, and salt efflorescence

Salt efflorescence is one of the major hazards to cultural heritages, masonries, and highways etc. It is now generally accepted that damages caused by salt efflorescence are mainly due to continuous cycles of salt crystallization/dissolution or hydration/dehydration in confined spaces. The position where salt efflorescence occurs and its type are closely related to the degree of damages caused by salt efflorescence. It is known that water is the key environmental factor determining the salt crystallization position. But influence of the correlation between water supply and evaporation on the position of salt crystallization is still not clearly understood. In this work, a set of experiments are designed to investigate salt efflorescence in porous matrix. It is found that the types and positions of salt efflorescence have little to do with nucleation, but are mainly governed by crystal growth, which is controlled by the rates of water evaporation, water and salt supply, capillary forces and surface properties of the porous matrices.

The rise and fall of adenine clusters in the gas phase: a glimpse into crystal growth and nucleation

The emergence of a crystal nucleus from disordered states is a critical and challenging aspect of the crystallization process, primarily due to the extremely short length and timescales involved. Methods such as liquid-cell or low-dose focal-series transmission electron microscopy (TEM) are often employed to probe these events. In this study, we demonstrate that ion mobility spectrometry-mass spectrometry (IMS-MS) offers a complementary and insightful perspective on the nucleation process by examining the sizes and shapes of small clusters, specifically those ranging from n = 2 to 40. Our findings reveal the significant role of sulfate ions in the growth of adeninediium sulfate clusters, which are the precursors to the formation of single crystals. Specifically, sulfate ions stabilize adenine clusters at the 1:1 ratio. In contrast, guanine sulfate forms smaller clusters with varied ratios, which become stable as they approach the 1:2 ratio. The nucleation size is predicted to be between n = 8 and 14, correlating well with the unit cell dimensions of adenine crystals. This correlation suggests that IMS-MS can identify critical nucleation sizes and provide valuable structural information consistent with established crystallographic data. We also discuss the strengths and limitations of IMS-MS in this context. IMS-MS offers rapid and robust experimental protocols, making it a valuable tool for studying the effects of various additives on the assembly of small molecules. Additionally, it aids in elucidating nucleation processes and the growth of different crystal polymorphs.

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.

Environmentally Friendly Photothermal Membranes for Halite Recovery from Reverse Osmosis Brine via Solar-Driven Membrane Crystallization

Modern society and industrial development rely heavily on the availability of freshwater and minerals. Seawater reverse osmosis (SWRO) has been widely adopted for freshwater supply, although many questions have arisen about its environmental sustainability owing to the disposal of hypersaline rejected solutions (brine). This scenario has accelerated significant developments towards the hybridization of SWRO with membrane distillation-crystallization (MD-MCr), which can extract water and minerals from spent brine. Nevertheless, the substantial specific energy consumption associated with MD-MCr remains a significant limitation. In this work, energy harvesting was secured from renewables by hotspots embodied in the membranes, implementing the revolutionary approach of brine mining via photothermal membrane crystallization (PhMCr). This method employs self-heating nanostructured interfaces under solar radiation to enhance water evaporation, creating a carefully controlled supersaturated environment responsible for the extraction of minerals. Photothermal mixed matrix photothermal membranes (MMMs) were developed by incorporating graphene oxide (GO) or carbon black (CB) into polyvinylidene fluoride (PVDF) solubilized in an eco-friendly solvent (i.e., triethyl phosphate (TEP)). MMMs were prepared using non-solvent-induced phase separation (NIPS). The effect of GO or GB on the morphology of MMMs and the photothermal behavior was examined. Light-to-heat conversion was used in PhMCr experiments to facilitate the evaporation of water from the SWRO brine to supersaturation, leading to sodium chloride (NaCl) nucleation and crystallization. Overall, the results indicate exciting perspectives of PhMCr in brine valorization for a sustainable desalination industry.

Structural Features and Zeolite Stability: A Linearized Equation Approach

Zeolite stability, in terms of lattice energy, is revisited from a crystal-chemistry point of view. A linearized equation relates the zeolite lattice energy using simple structural data readily available from experiments or modeling. The equation holds for a large range of zeolite energies, up to 3 eV per tetrahedron with respect to quartz, and has been validated internally via two simple machine learning automatic procedures for data fitting/reference partitions and externally using data from recently synthesized zeolites. The approach is certain in locating those recently synthesized zeolites in the energy range of those experimentally known zeolites used in the parametrization of the linearized equation. Hidden intrinsic structural data-energy correlations were found for data sets built from energy-relaxed structures along with energy values computed using the same energy functions employed in the structural relaxation. The asymmetry of the structural features is relevant for an accurate description of the energy.

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.

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.

Heterogeneous nucleation in the random field Ising model

We investigate the nucleation dynamics of the three-dimensional random field Ising model under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate.

Resolving Temperature-Dependent Hydrate Nucleation Pathway: The Role of "Transition Layer"

Understanding the nucleation of natural gas hydrate (NGH) at different conditions has important implications to NGH recovery and other industrial applications, such as gas storage and separation. Herein, vast numbers of hydrate nucleation events are traced via molecular dynamics (MD) simulations at different degrees of supercooling (or driving forces). Specifically, to precisely characterize a hydrate nucleus from an aqueous system during the MD simulation, we develop an evolutionary order parameter (OP) to recognize the nucleus size and shape. Subsequently, the free energy landscapes of hydrate during nucleation are explored by using the newly developed OP. The results suggest that at 270 K (or 0.92 Tm supercooling, where Tm is the melting point), the near-rounded nucleus prevails during the nucleation, as described from the classical nucleation theory. In contrast, at relatively strong driving forces of 0.85 and 0.88 Tm, nonclassical nucleation events arise. Specifically, the pathway toward an elongated nucleus becomes as important as the pathway toward a near-rounded nucleus. To explain the distinct nucleation phenomena at different supercoolings, a notion of a "transition layer" (or liquid-blob-like layer) is proposed. Here, the transition layer is to describe the interfacial region between the nucleus and aqueous solution, and this layer entails two functionalities: (1) it tends to retain CH4 depending on the degrees of supercooling and (2) it facilitates collision among CH4, which thus promote the incorporation of CH4 into nucleus. Our simulation indicates that compared to the near-rounded nucleus, the transition layer surrounding the elongated nucleus is more evident with the higher collision rate among CH4 molecules. As such, the transition layer tends to promote the elongated nucleus pathway, while offsetting the cost of larger surface free energy associated with the elongated nucleus. At 0.92 Tm, however, the transition layer gradually disappears, and classical nucleation events dominate. Overall, the notion of "transition layer" offers deeper insight into the NGH nucleation at different degrees of supercooling and could be extended to describe other types of hydrate nucleation.

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 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.

A Review of Laser-Induced Crystallization from Solution

Crystallization abounds in nature and industrial practice. A plethora of indispensable products ranging from agrochemicals and pharmaceuticals to battery materials are produced in crystalline form in industrial practice. Yet, our control over the crystallization process across scales, from molecular to macroscopic, is far from complete. This bottleneck not only hinders our ability to engineer the properties of crystalline products essential for maintaining our quality of life but also hampers progress toward a sustainable circular economy in resource recovery. In recent years, approaches leveraging light fields have emerged as promising alternatives to manipulate crystallization. In this review article, we classify laser-induced crystallization approaches where light-material interactions are utilized to influence crystallization phenomena according to proposed underlying mechanisms and experimental setups. We discuss nonphotochemical laser-induced nucleation, high-intensity laser-induced nucleation, laser trapping-induced crystallization, and indirect methods in detail. Throughout the review, we highlight connections among these separately evolving subfields to encourage the interdisciplinary exchange of ideas.

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.

Broken bond models, magic-sized clusters, and nucleation theory in nanoparticle synthesis

Magic clusters are metastable faceted nanoparticles that are thought to be important and, sometimes, observable intermediates in the nucleation of certain faceted crystallites. This work develops a broken bond model for spheres with a face-centered-cubic packing that form tetrahedral magic clusters. With just one bond strength parameter, statistical thermodynamics yield a chemical potential driving force, an interfacial free energy, and free energy vs magic cluster size. These properties exactly correspond to those from a previous model by Mule et al. [J. Am. Chem. Soc. 143, 2037 (2021)]. Interestingly, a Tolman length emerges (for both models) when the interfacial area, density, and volume are treated consistently. To describe the kinetic barriers between magic cluster sizes, Mule et al. invoked an energy parameter to penalize the two-dimensional nucleation and growth of new layers in each facet of the tetrahedra. According to the broken bond model, barriers between magic clusters are insignificant without the additional edge energy penalty. We estimate the overall nucleation rate without predicting the rates of formation for intermediate magic clusters by using the Becker-Döring equations. Our results provide a blueprint for constructing free energy models and rate theories for nucleation via magic clusters starting from only atomic-scale interactions and geometric considerations.

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.

Light-induced dissolution and concomitant crystallization of a Keggin-type polyoxometalate mimicking a naturally occurring phenomenon

A suspension of a yellow polycrystalline compound [PPh₄]₃[PMo^VI₁₂O₄₀] in N-methylformanilide (NMF) (in which it is not soluble), on irradiation with sunlight, initiates dissolution via its reduction followed by its crystallization leading to the isolation of single crystals of compound [PPh₄]₄[PMo^VMo^VI₁₁O₄₀]·3CH₃(C₆H₅)NCHO (1). Compounds [PPh₄]₃[PMo^VI₁₂O₄₀]·1.75 CH₃(C₆H₅)NCHO (2) and [PPh₄]₃[PMo^VI₁₂O₄₀]·2CH₃(C₆H₅)NCHO (3), each containing an oxidized Keggin anion, are obtained at two different temperatures when the corresponding mother liquor is kept in the dark.

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 of Biomolecular Condensates from Finite-Sized Simulations

The nucleation of protein condensates is a concentration-driven process of assembly. When modeled in the canonical ensemble, condensation is affected by finite-size effects. Here, we present a general and efficient route for obtaining ensemble properties of protein condensates in the macroscopic limit from finite-sized nucleation simulations. The approach is based on a theoretical description of droplet nucleation in the canonical ensemble and enables estimation of thermodynamic and kinetic parameters, such as the macroscopic equilibrium density of the dilute protein phase, the surface tension of the condensates, and nucleation free energy barriers. We apply the method to coarse-grained simulations of NDDX4 and FUS-LC, two phase-separating disordered proteins with different physicochemical characteristics. Our results show that NDDX4 condensate droplets, characterized by lower surface tension, higher solubility, and faster monomer exchange dynamics compared to those of FUS-LC, form with negligible nucleation barriers. In contrast, FUS-LC condensates form via an activated process over a wide range of concentrations.

Freeze desalination: Current research development and future prospects

Desalination is the solution for water security in regions with insufficient resources. This comes at high energy cost and hence improving desalination technologies translate into huge saving. Freeze desalination (FD) is emerging as an attractive low energy and less corrosion alternative to provide the needed fresh water. The maturity of the heat driven cooling technology and solar cooling have given freeze desalination an additional momentum. This paper summarizes the latest research progress done on FD that continues to push this technology towards deployment. It gives an overview of the FD configurations and highlighting its pros and cons, presents the recent experimental work that investigate the physics of the technology, and reviews the latest high-fidelity numerical modeling of brine freezing and salt diffusion away from crystal lattice which taps on the advanced development in computational power and multiphysics integration. This enables one to identify the challenges facing FD technology and stating the prospect and foreseeable research. The finding suggests that direct and indirect FD have been evolved well while the indirect is becoming the mainstream method for risk avoidance, while vacuum freezing and eutectic freezing are still facing large obstacles in their application. For direct FD, gas hydrate combined with liquefied natural gas (LNG) regasification has been popular topics to reduce their desalination cost. Simulation and modeling development in indirect FD continue to improve the knowledge of the mechanism of ice growth and salt entrapment which are key problems that need further experimental and numerical investigations. Nonetheless, the current successful application of LNG cold energy in freeze desalination, the hybridization of FD with conventional desalination technologies, as well as ultrasound assisted freezing are promising directions for FD commercialization.

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.

Obtaining Consistent Free Energies for Ion Binding at Surfaces from Solution: Pathways versus Alchemy for Determining Kink Site Stability

Ion incorporation or removal from a solid at the interface with solution is a fundamental part of crystal growth. Despite this, there have been few quantitative determinations of the thermodynamics for such processes from atomistic molecular dynamics due to the associated technical challenges. In this study, we compute the free energies for ion removal from kink sites at the interface between NaCl and water as an illustrative example. To examine the influence of the free energy technique used, we compare methods that follow an explicit pathway for dissolution with those that focus on the thermodynamics of the initial and final states using metadynamics and free energy perturbation, respectively. While the initial results of the two approaches are found to be completely different, it is demonstrated that the thermodynamics can be reconciled with appropriate corrections for the standard states, thus illustrating the need for caution in interpreting raw free energy curves for ion binding as widely found in the literature. In addition, a new efficient approach is introduced to correct for the system size dependence of kink site energies both due to the periodic interaction of charges in an inhomogeneous dielectric system and due to the dipolar interactions between pairs of kinks along a row. Ultimately, it is shown that with suitable care, both classes of free energy techniques are capable of producing kink site stabilities that are consistent with the solubility of the underlying bulk solid. However, the precise values for individual kink sites exhibit a small systematic offset, which can be ascribed to the contribution of the interfacial potential to the pathway-based results. For the case of NaCl, the free energies of the kink sites relative to a 1 M aqueous solution for Na⁺ and Cl^- are found to be surprisingly different and of opposite sign, despite the ions having very similar hydration free energies.

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.

In situ optical spectroscopy of crystallization: One crystal nucleation at a time

While crystallization is a ubiquitous and an important process, the microscopic picture of crystal nucleation is yet to be established. Recent studies suggest that the nucleation process can be more complex than the view offered by the classical nucleation theory. Here, we implement single crystal nucleation spectroscopy (SCNS) by combining Raman microspectroscopy and optical trapping induced crystallization to spectroscopically investigate one crystal nucleation at a time. Raman spectral evolution during a single glycine crystal nucleation from water, measured by SCNS and analyzed by a nonsupervised spectral decomposition technique, uncovered the Raman spectrum of prenucleation aggregates and their critical role as an intermediate species in the dynamics. The agreement between the spectral feature of prenucleation aggregates and our simulation suggests that their structural order emerges through the dynamic formation of linear hydrogen-bonded networks. The present work provides a strong impetus for accelerating the investigation of crystal nucleation by optical spectroscopy.

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.

Graphitic-like Hexagonal Phase of Alkali Halides in Quasi-Two-Dimensional Confined Space under Ambient Conditions

The discovery of specific matter phases with abnormal physical properties in low-dimensional systems and/or on particular substrates, such as the hexagonal phase of ice and two-dimensional (2D) CaCl with an abnormal valence state, continuously reveals more fundamental mechanisms of the nature. Alkali halides, represented by NaCl, are one of the most common compounds and usually thought to be well-understood. In the past decades, many theoretical studies suggested the existence of one particular phase, that is, the graphitic-like hexagonal phase of alkali halides at high pressure or in low-dimension states, with the expectation of improved properties of this matter phase but lacking experimental evidence due to severe technical challenges. Here, by optimized cryo-electron microscopy, we report the direct atomic-resolution observation and in situ characterization of the prevalent and stable graphitic-like alkali halide hexagonal phases, which were spontaneously formed by unsaturated NaCl and LiCl solution, respectively, in the quasi-2D confined space between reduced graphene oxide layers under ambient conditions. Combined with a control experiment, density functional theory calculations, and previous theoretical studies, we believe that a delicate balance among the cation-π interaction of the solute and substrate, electrostatic interactions of anions and cations, solute-solvent interactions, and thermodynamics under confinement synergistically results in the formation of such hexagonal crystalline phases. These findings highlight the effects of the substrate and the confined space on the formation of specific matter phases and provide a universal scheme for the preparation of special graphitic-like hexagonal phases of alkali halides.

Photocatalytic membrane reactors for produced water treatment and reuse: Fundamentals, affecting factors, rational design, and evaluation metrics

Treatment and reuse of produced water (PW), the largest wastewater stream generated during oil and gas production, provides a promising option to address the increasing clean water demands. High-performance treatment technologies are needed to efficiently remove the organic and inorganic contaminants in PW for fit-for-purpose applications. Photocatalytic membrane reactor (PMR) is an emerging green technology for removal of organic pollutants, photoreduction of heavy metals, photo-inactivation of bacteria, and resource recovery. This study critically reviewed the mechanisms of photocatalysis and membrane processes in PMR, factors affecting PMR performance, rational design, and evaluation metrics for PW treatment. Specifically, PW characteristics, photocatalysts properties, membranes applied, and operating conditions are of utmost importance for rational design and reliable operation of PMR. PW pretreatment to remove oil and grease, colloidal and suspended solids is necessary to reduce membrane fouling and ensure optimal PMR performance. The metrics to evaluate PMR performance were developed including light utilization, exergetic efficiency, water recovery, product water improvement, lifetime of the photocatalyst, and costs. This review also presented the research gaps and outlook for future research.

Membrane distillation crystallization technology for zero liquid discharge and resource recovery: Opportunities, challenges and futuristic perspectives

Water resources are getting limited, which emphasises the need for the reuse of wastewater. The conventional waste(water) treatment methods such as reverse osmosis (RO) and multi-effect distillation (MED) are rendered limited due to certain limitations. Moreover, the imposition of stringent environmental regulations in terms of zero liquid discharge (ZLD) of wastewater containing very high dissolved solids has assisted in developing technologies for the recovery of water and useful solids. Membrane distillation crystallization (MDCr) is an emerging hybrid technology synergising membrane distillation (MD) and crystallization, thus achieving ZLD. MDCr technology can be applied to desalinate seawater, treat nano-filtration, and RO reject brine and industrial wastewater to increase water recovery and yield useful solids. This manuscript focuses on recent advances in MDCr, emphasizing models that account for application in (waste)water treatment. MDCr has dual benefits, first the environmental conservation due to non-disposal of wastewater and second, resources recovery proving the proverb that waste is a misplaced resource. Limitations of standalone MD and crystallization are discussed to underline the evolution of MDCr. In this review, MDCr's ability and feasibility in the treatment of industrial wastewater are highlighted. This manuscript also examines the operational issues, including crystal deposition (scaling) on the membrane surface, pore wetting phenomenon and economic consequences (energy use and operating costs). Finally, opportunities and future prospects of the MDCr technology are discussed. MDCr technology can amplify natural resources availability by recovering freshwater and useful minerals from the waste stream, thus compensating for the relatively high cost of the technology.

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 rate in the two dimensional Ising model in the presence of random impurities

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from the Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy of the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.

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.

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.

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.

Dissimilarity measure of local structure in inorganic crystals using Wasserstein distance to search for novel phosphors

To efficiently search for novel phosphors, we propose a dissimilarity measure of local structure using the Wasserstein distance. This simple and versatile method provides the quantitative dissimilarity of a local structure around a center ion. To calculate the Wasserstein distance, the local structures in crystals are numerically represented as a bag of interatomic distances. The Wasserstein distance is calculated for various ideal structures and local structures in known phosphors. The variation of the Wasserstein distance corresponds to the structural variation of the local structures, and the Wasserstein distance can quantitatively explain the dissimilarity of the local structures. The correlation between the Wasserstein distance and the full width at half maximum suggests that candidates for novel narrow-band phosphors can be identified by crystal structures that include local structures with small Wasserstein distances to local structures of known narrow-band phosphors. The quantitative dissimilarity using the Wasserstein distance is useful in the search of novel phosphors and expected to be applied in materials searches in other fields in which local structures play an important role.

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.