Vapor Pressure of Water Nanodroplets

Abnormal condensation of water vapour at ambient temperature

The homogeneous condensation of water vapor at ambient temperature is studied using molecular dynamics simulation. We reveal that there is a droplet size at the nanoscale where water droplets can be stabilized in the condensation process. Our simulations show that the growth of water droplets is dominated by collision and coagulation between small water droplets after nucleation. This process is found to be accompanied by exceptionally fast evaporation such that droplet growth is balanced by evaporation when water droplets grow to a critical size, approximately 12.5 Å in radius, reaching a stable size distribution. The extremely high evaporation rate is attributed to the curvature dependence of surface tension. Surface tension shows a significant decrease with decreasing droplet size below 20 Å, which causes the total free energy of nanoscaled water droplets to rise after collision and coagulation. Consequently, water droplets have to shrink via fast evaporation. The curvature dependence of surface tension is related to the dielectric ordering of water molecules near the surface of water droplets. Owing to fast evaporation, secondary condensation occurs, and many small water clusters form, ultimately exhibiting a bimodal distribution of water-droplet size.

Harvesting Energy from Changes in Relative Humidity Using Nanoscale Water Capillary Bridges

We show that nanoscale water capillary bridges (WCB) formed between patchy surfaces can extract energy from the environment when subjected to changes in relative humidity (RH). Our results are based on molecular dynamics simulations combined with a modified version of the Laplace-Kelvin equation, which is validated using the nanoscale WCB. The calculated energy density harvested by the nanoscale WCB is relevant, ≈1700 kJ/m3, and is comparable to the energy densities harvested using available water-responsive materials that expand and contract due to changes in RH.

A comprehensive review on the behavior and evolution of oil droplets during oil/water separation by membranes

Membrane separation technology has significant advantages for treating oil-in-water emulsions. Understanding the evolution of oil droplets could reveal the interfacial and colloidal interactions, facilitate the design of advanced membranes, and improve the separation performances. This review on the characteristic behavior and evolution of oil droplets focuses on the advanced analytical techniques, and the subsequent fouling as well as demulsification effects during membrane separation. A detailed introduction is provided on microscopic observations and numerical simulations of the dynamic evolution of oil droplets, featuring real-time in-situ visualization and accurate reconstruction, respectively. Characteristic behaviors of these oil droplets include attachment, pinning, wetting, spreading, blockage, intrusion, coalescence, and detachment, which have been quantified by specific proposed parameters and criteria. The fouling process can be evaluated using Hermia and resistance models. The related adhesion force and intrusion pressure as well as droplet-droplet/membrane interfacial interactions can be accurately quantified using various force analysis methods and advanced force measurement techniques. It is encouraging to note that oil coalescence has been achieved through various effects such as electrostatic interactions, mechanical actions, Laplace pressure/surface free energy gradients, and synergistic effects on functional membranes. When oil droplets become destabilized and coalesce into larger ones, the functional membranes can overcome the limitations of size-sieving effect to attain higher separation efficiency. This not only bypasses the trade-off between permeability and rejection, but also significantly reduces membrane fouling. Finally, the challenges and potential research directions in membrane separation are proposed. We hope this review will support the engineering of advanced materials for oil/water separation and research on interface science in general.

Nanobubble Stability and Formation on Solid-Liquid Interfaces in Open Environments

Are surface nanobubbles transient or thermodynamically stable structures? This question remained controversial until recently, when the stability of gas nanobubbles at solid-liquid interfaces was demonstrated from thermodynamic arguments in closed systems, establishing that bubbles with radii of hundreds of nanometers can be stable at modest supersaturations if the gas amount is finite. Here we develop a grand-canonical description of bubble formation that predicts that nanobubbles can nucleate and remain thermodynamically stable in open boundaries at high supersaturations when pinned to hydrophobic supports as small as a few nanometers. While larger bubbles can also be stable at lower supersaturations, the corresponding barriers are orders of magnitude above kT, meaning that their formation cannot proceed via heterogeneous nucleation on a uniform solid interface but must follow some alternative path. Moreover, we conclude that a source of growth-limiting mechanism, such as pinning or gas availability, is necessary for the thermodynamic stabilization of surface bubbles.

Diameter-Optimum Spreading for the Impinging of Water Nanodroplets on Solid Surfaces

The impinging of water nanodroplets on solid surfaces is crucial to many nanotechnologies. Through large-scale molecular dynamics simulations, the size effect on the spreading of water nanodroplets after impinging on hydrophilic, graphite, and hydrophobic surfaces under low impinging velocities has been systematically studied. The spreading rates of nanodroplets first increase and then decrease and gradually become constant with the increase of nanodroplet diameter. The nanodroplets with the diameters of 17-19 nm possess the highest spreading rates because of the combined effect of the strongest interfacial interaction and the strongest surface interaction within water molecules. The highest water molecule densities, hydrogen bond numbers, and dielectric constants of interface and surface layers mainly contribute to the lowest interface work of adhesion and surface tension values at optimal diameters. These results unveil the nonmonotonic characteristics of spreading velocity, interface work of adhesion and surface tension with nanodroplet diameter for nanodroplets on solid surfaces.

Confined Electrochemical Behaviors of Single Platinum Nanoparticles Revealing Ultrahigh Density of Gas Molecules inside a Nanobubble

Understanding the basic physicochemical properties of gas molecules confined within nanobubbles is of fundamental importance for chemical and biological processes. Here, we successfully monitored the nanobubble-confined electrochemical behaviors of single platinum nanoparticles (PtNPs) at a carbon fiber ultramicroelectrode in HClO₄ and H₂O₂ solution. Due to the catalytic decomposition of H₂O₂, a single oxygen nanobubble was formed on individual PtNPs to block the active surface of particles for proton reduction and to suppress their stochastic motion, resulting in significantly distinguished current traces. Furthermore, the combination of theoretical calculations and high-resolution electrochemical measurements allowed the nanobubble size and the oxygen gas density inside a single nanobubble to be quantified. Moreover, the ultrahigh oxygen density inside (1046 kg/m³) was revealed, indicating that gas molecules in a nanosized space existed with a high state of aggregation. Our approach sheds light on the gas aggregation behaviors of nanoscale bubbles using single-entity electrochemical measurements.

Partition Constant of Binary Mixtures for the Equilibrium between a Bulk and a Confined Phase

It is well-known that the thermodynamic, kinetic and structural properties of fluids, and in particular of water and its solutions, can be drastically affected in nanospaces. A possible consequence of nanoscale confinement of a solution is the partial segregation of its components. Thereby, confinement in nanoporous materials (NPM) has been proposed as a means for the separation of mixtures. In fact, separation science can take great advantage of NPM due to the tunability of their properties as a function of nanostructure, morphology, pore size, and surface chemistry. Alcohol-water mixtures are in this context among the most relevant systems. However, a quantitative thermodynamic description allowing for the prediction of the segregation capabilities as a function of the material-solution characteristics is missing. In the present study we attempt to fill this vacancy, by contributing a thermodynamic treatment for the calculation of the partition coefficient in confinement. Combining the multilayer adsorption model for binary mixtures with the Young equation, we conclude that the liquid-vapor surface tension and the contact angle of the pure substances can be used to predict the separation ability of a particular material for a given mixture to a semiquantitative extent. Moreover, we develop a Kelvin-type equation that relates the partition coefficient to the radius of the pore, the contact angle, and the liquid-vapor surface tensions of the constituents. To assess the validity of our thermodynamic formulation, coarse grained molecular dynamics simulations were performed on models of alcohol-water mixtures confined in cylindrical pores. To this end, a coarse-grained amphiphilic molecule was parametrized to be used in conjunction with the mW potential for water. This amphiphilic model reproduces some of the properties of methanol such as enthalpy of vaporization and liquid-vapor surface tension, and the minimum of the excess enthalpy for the aqueous solution. The partition coefficient turns out to be highly dependent on the molar fraction, on the interaction between the components and the confining matrix, and on the radius of the pore. A remarkable agreement between the theory and the simulations is found for pores of radius larger than 15 Å.

Salt Enrichment and Dynamics in the Interface of Supercooled Aqueous Droplets

The interconversion reaction of NaCl between the contact-ion pair (CIP) and the solvent-separated ion pair (SSIP) as well as the free-ion state in cold droplets has not yet been investigated. We report direct computational evidence that the lower is the temperature, the closer to the surface the ion interconversion reaction takes place. In supercooled droplets the enrichment of the subsurface in salt becomes more evident. The stability of the SSIP relative to the CIP increases as the ion-pairing is transferred toward the droplet's outer layers. In the free-ion state, where the ions diffuse independently in the solution, the number density of Cl^- shows a broad maximum in the interior in addition to the well-known maximum in the surface. In the study of the reaction dynamics, we find a weak coupling between the interionic NaCl distance reaction coordinate and the solvent degrees of freedom, which contrasts with the diffusive crossing of the free energy barrier found in bulk solution modeling. The H₂O self-diffusion coefficient is found to be at least an order of magnitude larger than that in the bulk solution. We propose to exploit the enhanced surface ion concentration at low temperature to eliminate salts from droplets in native mass spectrometry ionization methods.

The coexistence curve and surface tension of a monatomic water model

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid-vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid-vapor critical point at T_c = 917.6 K, ρ_c = 0.311 g cm^-3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water.

Extension of Kelvin's equation to dipolar colloids

Suspensions of colloids driven out-of-equilibrium demonstrate interesting collective behavior, such as organized and directed clustering and swarming. These systems require continuous energy input, yet some of the dynamics of these driven systems resemble the equilibrium-phase behavior of molecular fluids, such as crystallization, condensation, and phase separation. Consequently, there has been significant interest in exploring the applicability of thermodynamic concepts, such as pressure and surface tension, to describe nonequilibrium phenomena. Here, we show how rotating magnetic fields can drive superparamagnetic particles to form steady-state vapor–liquid coexistence that can be analyzed with Kelvin’s equation to determine an “effective vapor pressure” for this active colloidal system. These results illustrate the convergence of statistical physics of simple liquids to nonequilibrium colloidal fluids.

Vapor pressure refers to the pressure exerted by the vapor phase in thermodynamic equilibrium with either its liquid or solid phase. An important class of active matter is field-driven colloids. A suspension of dipolar colloids placed in a high-frequency rotating magnetic field undergoes a nonequilibrium phase transition into a dilute and dense phase, akin to liquid–vapor coexistence in a simple fluid. Here, we compute the vapor pressure of this colloidal fluid. The number of particles that exist as the dilute bulk phase versus condensed cluster phases can be directly visualized. An exponential relationship between vapor pressure and effective temperature is determined as a function of applied field strength, analogous to the thermodynamic expression between vapor pressure and temperature found for pure liquids. Additionally, we demonstrate the applicability of Kelvin’s equation to this field-driven system. In principle, this appears to be in conflict with macroscopic thermodynamic assumptions due to the nonequilibrium and discrete nature of this colloidal system. However, the curvature of the vapor–liquid interface provides a mechanical equilibrium characterized by interfacial tension that connects the condensed clusters observed with these active fluids to classical colligative fluid properties.

Unraveling the Interaction of Water-in-Oil Emulsion Droplets via Molecular Simulations and Surface Force Measurements

Water-in-oil emulsions widely exist in various chemical and petroleum engineering processes, and their stabilization and destabilization behaviors have attracted much attention. In this work, molecular dynamic (MD) simulations were conducted on the water-in-oil emulsion droplets with the presence of surface-active components, including a polycyclic aromatic compound (VO-79) and two nonionic surfactants: the PEO₅PPO₁₀PEO₅ triblock copolymer and Brij-93. At the surface of water droplets, films were formed by the adsorbate molecules that redistributed during the approaching of the droplets. The redistribution of PEO₅PPO₁₀PEO₅ was more pronounced than that of Brij-93 and VO-79, which contributed to lower repulsion during coalescence. The interaction forces during droplet coalescence were also measured using atomic force microscopy. Jump-in phenomenon and coalescence were observed for systems with VO-79, Brij-93, and a low concentration of Pluronic P123. The critical force before jump-in was lowest for the low concentration of Pluronic P123, consistent with the MD results. Adhesion was measured when separating water droplets with a high concentration of Pluronic P123. By correlating theoretical simulations and experimental force measurements, this work improves the fundamental understanding on the interaction behaviors of water droplets in an oil medium in the presence of interface-active species and provides atomic-level insights into the stabilization and destabilization mechanisms of water-in-oil emulsion.

Surface thermodynamics at the nanoscale

Fluid interfaces with nanoscale radii of curvature are generating great interest, both for their applications and as tools to probe our fundamental understanding. One important question is what is the smallest radius of curvature at which the three main thermodynamic combined equilibrium equations are valid: the Kelvin equation for the effect of curvature on vapor pressure, the Gibbs-Thomson equation for the curvature-induced freezing point depression, and the Ostwald-Freundlich equation for the curvature-induced increase in solubility. The objective of this Perspective is to provide conceptual, molecular modeling, and experimental support for the validity of these thermodynamic combined equilibrium equations down to the smallest interfacial radii of curvature. Important concepts underpinning thermodynamics, including ensemble averaging and Gibbs's treatment of bulk phase heterogeneities in the region of an interface, give reason to believe that these equations might be valid to smaller scales than was previously thought. There is significant molecular modeling and experimental support for all three of the Kelvin equation, the Gibbs-Thomson equation, and the Ostwald-Freundlich equation for interfacial radii of curvature from 1 to 4 nm. There is even evidence of sub-nanometer quantitative accuracy for the Kelvin equation and the Gibbs-Thomson equation.

Direct measurement of curvature-dependent surface tension of an alcohol nanomeniscus

Surface tension is a key parameter for understanding nucleation in the very initial stage of phase transformation. Although surface tension has been predicted to vary with the curvature of the liquid-vapor interface, particularly at the large curvature of, e.g., the subnanometric critical nucleus, experimental study still remains challenging due to inaccessibility to such a small cluster. Here, by directly measuring the critical size of a single capillary-condensed nanomeniscus using atomic force microscopy, we address the curvature dependence of surface tension of alcohols and observe that the surface tension is doubled for ethanol and n-propanol with a radius-of-curvature of ∼-0.46 nm. We also find that the interface of larger negative (positive) curvature exhibits larger (smaller) surface tension, which evidently governs nucleation at the ∼1 nm scale and below, indicating more facilitated nucleation than normally expected. Such well characterized curvature effects contribute to better understanding and accurate analysis of nucleation occurring in various fields including materials science and atmospheric science.

Interfacial thermodynamics of spherical nanodroplets: molecular understanding of surface tension via a hydrogen bond network

Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. In particular, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory and find that surface tension decreases appreciably below 1 nm radius, whose analytical expression is consistently derived from the classic Tolman's equation. In particular, the free energy analysis of nanodroplets shows that the change of surface tension originates dominantly from the configurational energy of interfacial molecules, which is evidenced by the increasingly disrupted hydrogen bond network as the droplet size decreases. Our result can be applied to the interface-related phenomena associated with molecular fluctuations such as biomolecule adsorption at the sub-nm scale where macroscopic thermodynamic quantities are ill-defined.

Electrochemically Generated Nanobubbles: Invariance of the Current with Respect to Electrode Size and Potential

Gas-producing electrochemical reactions are key to energy conversion and generation technologies. Bubble formation dramatically decreases gas-production rates on nanoelectrodes, by confining the reaction to the electrode boundary. This results in the collapse of the current to a stationary value independent of the potential. Startlingly, these residual currents also appear to be insensitive to the nanoelectrode diameter in the 5 to 500 nm range. These results are counterintuitive, as it may be expected that the current be proportional to the circumference of the electrode, i.e., the length of the three-phase line where the reaction occurs. Here, we use molecular simulations and a kinetic model to elucidate the origin of current insensitivity with respect to the potential and establish its relationship to the size of nanoelectrodes. We provide critical insights for the design and operation of nanoscale electrochemical devices and demonstrate that nanoelectrode arrays maximize conversion rates compared to macroscopic electrodes with same total area.

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

Liquid-vapor surface tension (ST) in nanopores attracts great attention in many industries because of the prosperity of nanoscience and nanotechnology. Here, considering the important emerging new physical phenomena induced by nanoconfinement effects, including curvature-dependent and shift-critical temperature (T_c)-dependent effects, the anomalous variation of ST in nanopores is captured from the molecular potential perspective. Furthermore, a simple analytical model is proposed to determine the ST in nanopores by correlating these two effects with an easily accessible parameter, that is, normalized pore dimension, which is the ratio of the pore radius to Lennard-Jones size parameter. The model is validated to be reliable for determining the STs of different substances both in the bulk phase as well as nanopores through comparison with the experimental results and molecular simulations. Our results show that the reduction of ST induced by the nanoconfinement effects is visible when the pore diameter is within tens of nanometers, and the reduction is more sensitive as the pore size decreases. In detail, the curvature-dependent effect is remarkable in the pores with diameters ranging from a few nanometers to tens of nanometers. Moreover, a simply generalized formula is obtained to determine the curvature-dependent effect and the Tolman length for different substances. The shift-T_c-dependent effect is not only related to the pore dimension but also depends on the temperature. As the pore size decreases, the critical temperature of confined fluids diverges significantly from the bulk values. While at high temperatures, the range of pore size impacted by the shift-Tc-dependent effect is enlarged. Additionally, the nanoconfined STs of different substances are calculated and compared. Overall, the new model captures the underlying physics behind the variation of STs in nanopores and can determine the nanoconfined STs reasonably. Moreover, the simple formulation of the model is beneficial to the practical applications in many chemical engineering processes, such as chemical separation, nucleation phenomenon, and capillary condensation.

Direct observation of anisotropic growth of water films on minerals driven by defects and surface tension

Knowledge of the occurrences of water films on minerals is critical for global biogeochemical and atmospheric processes, including element cycling and ice nucleation. The underlying mechanisms controlling water film growth are, however, misunderstood. Using infrared nanospectroscopy, amplitude-modulated atomic force microscopy, and molecular simulations, we show how water films grow from water vapor on hydrophilic mineral nanoparticles. We imaged films with up to four water layers that grow anisotropically over a single face. Growth usually begins from the near edges of a face where defects preferentially capture water vapor. Thicker films produced by condensation cooling completely engulf nanoparticles and form thicker menisci over defects. The high surface tension of water smooths film surfaces and produces films of inhomogeneous thickness. Nanoscale topography and film surface energy thereby control anisotropic distributions and thicknesses of water films on hydrophilic mineral nanoparticles.

Sparked Reduced Graphene Oxide for Low-Temperature Sodium-Beta Alumina Batteries

Wetting Na metal on the solid electrolyte of a liquid Na battery determines the operating temperature and performance of the battery. At low temperatures below 200 °C, liquid Na wets poorly on a solid electrolyte near its melting temperature (T_m = 98 °C), limiting its suitability for use in low-temperature batteries used for large-scale energy-storage systems. Herein, we propose the use of sparked reduced graphene oxide (rGO) that can improve the Na wetting in sodium-beta alumina batteries (NBBs), allowing operation at lower temperatures. Experimental and computational studies indicated rGO layers with nanogaps exhibited complete liquid Na wetting regardless of the surface energy between the liquid Na and the graphene oxide, which originated from the capillary force in the gap. Employing sparked rGO significantly enhanced the cell performance at 175 °C; the cell retained almost 100% Coulombic efficiency after the initial cycle, which is a substantial improvement over cells without sparked rGO. These results suggest that coating sparked rGO is a promising but simple strategy for the development of low-temperature NBBs.

How Do Surfactants Control the Agglomeration of Clathrate Hydrates?

Clathrate hydrates can spontaneously form under typical conditions found in oil and gas pipelines. The agglomeration of clathrates into large solid masses plugs the pipelines, posing adverse safety, economic, and environmental threats. Surfactants are customarily used to prevent the aggregation of clathrate particles and their coalescence with water droplets. It is generally assumed that a large contact angle between the surfactant-covered clathrate and water is a key predictor of the antiagglomerant performance of the surfactant. Here we use molecular dynamic simulations to investigate the structure and dynamics of surfactant films at the clathrate-oil interface, and their impact on the contact angle and coalescence between water droplets and hydrate particles. In agreement with the experiments, the simulations predict that surfactant-covered clathrate-oil interfaces are oil wet but super-hydrophobic to water. Although the water contact angle determines the driving force for coalescence, we find that a large contact angle is not sufficient to predict good antiagglomerant performance of a surfactant. We conclude that the length of the surfactant molecules, the density of the interfacial film, and the strength of binding of its molecules to the clathrate surface are the main factors in preventing the coalescence and agglomeration of clathrate particles with water droplets in oil. Our analysis provides a molecular foundation to guide the molecular design of effective clathrate antiagglomerants.

Polymeric nanodroplets: an emerging trend in gaseous delivery system

Currently, nanotechnology-based products are gaining tremendous interest in the development of nanocarriers for drug delivery and nano-diagnostic devices. Nanodroplets (NDs) emerge as novel carriers for delivery of gases and actives with a wide range of applications in fields of theranostics, drug delivery and diagnostic devices. NDs are multifunctional carriers composed of an outer shell of drug and polymer that encapsulates the inner core of gases and liquid molecules. This review focuses on properties of NDs, mathematical theories, different polymers used in the preparation of NDs, characterisation, animal models, toxicity and applications of NDs. These nanocarriers are advantageous due to their cost-effectiveness and compatibility with both gaseous and liquid core molecules. NDs are increasingly utilised in the field of healthcare due to their properties like large effective surface area for drug loading and target specificity. These nanocarriers are also employed in the treatment of hypoxia, multiple sclerosis and cancer. In the near future, NDs will advance in fields of personalised medicine and precise theranostics.

Volatility of Amorphous Solid Water

Amorphous solid water is probably the most abundant form of solid water in the universe. Its saturation vapor pressure and thermodynamic properties, however, are not well known. We have investigated the saturation vapor pressure over vapor-deposited amorphous ice at temperatures between 133 and 147 K using a novel experimental method. The new method determines the absolute vapor pressures and the sublimation rates by measuring the mass growth rates of ice-covered nanoparticles under supersaturated water vapor conditions. We find that the vapor pressure of amorphous solid water is up to a factor of 3 higher than that predicted by current parameterizations, which are based in part on calorimetric measurements. We demonstrate that the calorimetric measurements can be reconciled with our data by acknowledging the formation of nanocrystalline ice as an intermediate ice phase during the crystallization of amorphous ice. As a result, we propose a new value for the enthalpy of crystallization of amorphous solid water of Δ H = 2312 ± 227 J/mol, which is about 1000 J/mol higher than the current consensus. Our results shine a new light on the abundance of water ice clouds on Mars and mesospheric clouds on Earth and may alter our understanding of ice formation in the stratosphere.

Size and shape dependency of the surface energy of metallic nanoparticles: unifying the atomic and thermodynamic approaches

Surface energy is a fundamental property of metallic nanoparticles (MeNPs), which plays a crucial role in nucleation and growth and has strong implications for the application and environmental impact of MeNPs. Surface energy (J m-2) can be size dependent, but experimental data on surface energy trends for MeNPs are inconclusive. Computational chemistry may resolve the issue, but the location and area of the surface used for scaling, which dramatically influences the outcome and interpretation, has not been properly investigated. The size dependency of the surface energy can only be determined by scaling to the thermodynamic surface of tension. To identify this, we have derived a generalized Tolman approach for non-spherical particles, which is used to analyze the thermodynamic consistency of various surface definitions. Only the physical surface, defined here, is consistent with the surface of tension. Scaling of recent computational data for faceted MeNPs to this surface yields a low size dependency of surface energy, in good agreement with the Tolman lengths corresponding to its interfacial position. We find Tolman lengths of -0.03 nm for icosahedra and -0.04 nm for cuboctahedra of gold or silver. With this result, our approach can be used to quantify the twinning energy for icosahedral nanoparticles, being ∼0.06 J per m2 twin area. To understand the unorthodox negative Tolman lengths, we have analyzed the surface energetics of the solid-gas interface of metals in relation to the liquid-vapor interface of water. Surface entropy is found to be imperative in determining the size dependence of surface free energy. At room temperature, the influence of surface entropy on surface enthalpy is much smaller for metals than for water. It explains why these two interfaces have opposite size dependencies of the surface Gibbs free energy and opposite signs of the Tolman length. For water, forming nanodroplets or nanobubbles, the Tolman length is negative (∼-0.014 nm) for the surface enthalpy, but positive (∼+0.06 ± 0.02 nm) for the surface Gibbs free energy. For MeNPs at room temperature, both entities are negative, but at high temperature, the increased surface entropy term may cause the size dependency of surface Gibbs free energy to become reversed.

Thermodynamic and structural anomalies of water nanodroplets

Liquid water nanodroplets are important in earth's climate, and are valuable for studying supercooled water because they resist crystallisation well below the bulk freezing temperature. Bulk liquid water has well-known thermodynamic anomalies, such as a density maximum, and when supercooled is hypothesised to exhibit a liquid-liquid phase transition (LLPT) at elevated pressure. However, it is not known how these bulk anomalies might manifest themselves in nanodroplets. Here we show, using simulations of the TIP4P/2005 water model, that bulk anomalies occur in nanodroplets as small as 360 molecules. We also show that the Laplace pressure inside small droplets reaches 220 MPa at 180 K, conditions close to the LLPT of TIP4P/2005. While the density and pressure inside nanodroplets coincide with bulk values at moderate supercooling, we show that deviations emerge at lower temperature, as well as significant radial density gradients, which arise from and signal the approach to the LLPT.

Grand Canonical Investigation of the Quasi Liquid Layer of Ice: Is It Liquid?

In this study, the solid-vapor equilibrium and the quasi liquid layer (QLL) of ice Ih exposing the basal and primary prismatic faces were explored by means of grand canonical molecular dynamics simulations with the monatomic mW potential. For this model, the solid-vapor equilibrium was found to follow the Clausius-Clapeyron relation in the range examined, from 250 to 270 K, with a Δ H_sub of 50 kJ/mol in excellent agreement with the experimental value. The phase diagram of the mW model was constructed for the low pressure region around the triple point. The analysis of the crystallization dynamics during condensation and evaporation revealed that, for the basal face, both processes are highly activated, and in particular cubic ice is formed during condensation, producing stacking-disordered ice. The basal and primary prismatic surfaces of ice Ih were investigated at different temperatures and at their corresponding equilibrium vapor pressures. Our results show that the region known as QLL can be interpreted as the outermost layers of the solid where a partial melting takes place. Solid islands in the nanometer length scale are surrounded by interconnected liquid areas, generating a bidimensional nanophase segregation that spans throughout the entire width of the outermost layer even at 250 K. Two approaches were adopted to quantify the QLL and discussed in light of their ability to reflect this nanophase segregation phenomena. Our results in the μVT ensemble were compared with NPT and NVT simulations for two system sizes. No significant differences were found between the results as a consequence of model system size or of the working ensemble. Nevertheless, certain advantages of performing μVT simulations in order to reproduce the experimental situation are highlighted. On the one hand, the QLL thickness measured out of equilibrium might be affected because of crystallization being slower than condensation. On the other, preliminary simulations of AFM indentation experiments show that the tip can induce capillary condensation over the ice surface, enlarging the apparent QLL.

What Controls the Limit of Supercooling and Superheating of Pinned Ice Surfaces?

Cold-adapted organisms produce antifreeze proteins and glycoproteins to control the growth, melting and recrystallization of ice. It has been proposed that these molecules pin the crystal surface, creating a curvature that arrests the growth and melting of the crystal. Here we use thermodynamic modeling and molecular simulations to demonstrate that the curvature of the superheated or supercooled surface depends on the temperature and distances between ice-binding molecules, but not the details of their interactions with ice. We perform simulations of ice pinned with the antifreeze protein TmAFP, polyvinyl alcohol with different degrees of polymerization, and model ice-binding molecules to determine the thermal hystereses on melting and freezing, i.e. the maximum curvature that can be attained before, respectively, ice melts or grows irreversibly over the ice-binding molecules. We find that the thermal hysteresis is controlled by the bulkiness of the ice-binding molecules and their footprint at the ice surface. We elucidate the origin of the asymmetry between freezing and melting hysteresis found in experiments and propose guidelines to design synthetic antifreeze molecules with potent thermal hysteresis activity.

Promotion of Homogeneous Ice Nucleation by Soluble Molecules

Atmospheric aerosols nucleate ice in clouds, strongly impacting precipitation and climate. The prevailing consensus is that ice nucleation is promoted heterogeneously by the surface of ice nucleating particles in the aerosols. However, recent experiments indicate that water-soluble molecules, such as polysaccharides of pollen and poly(vinyl alcohol) (PVA), increase the ice freezing temperature. This poses the question of how do flexible soluble molecules promote the formation of water crystals, as they do not expose a well-defined surface to ice. Here we use molecular simulations to demonstrate that PVA promotes ice nucleation through a homogeneous mechanism: PVA increases the nucleation rate by destabilizing water in the solution. This work demonstrates a novel paradigm for understanding ice nucleation by soluble molecules and provides a new handle to design additives that promote crystallization.

Abnormal gas-liquid-solid phase transition behaviour of water observed with in situ environmental SEM

Gas-liquid-solid phase transition behaviour of water is studied with environmental scanning electron microscopy for the first time. Abnormal phenomena are observed. At a fixed pressure of 450 Pa, with the temperature set to −7 °C, direct desublimation happens, and ice grows continuously along the substrate surface. At 550 Pa, although ice is the stable phase according to the phase diagram, metastable liquid droplets first nucleate and grow to ~100–200 μm sizes. Ice crystals nucleate within the large sized droplets, grow up and fill up the droplets. Later, the ice crystals grow continuously through desublimation. At 600 Pa, the metastable liquid grows quickly, with some ice nuclei floating in it, and the liquid-solid coexistence state exists for a long time. By lowering the vapour pressure and/or increasing the substrate temperature, ice sublimates into vapour phase, and especially, the remaining ice forms a porous structure due to preferential sublimation in the concave regions, which can be explained with surface tension effect. Interestingly, although it should be forbidden for ice to transform into liquid phase when the temperature is well below 0 °C, liquid like droplets form during the ice sublimation process, which is attributed to the surface tension effect and the quasiliquid layers.

Stability and Vapor Pressure of Aqueous Aggregates and Aerosols Containing a Monovalent Ion

The incidence of charged particles on the nucleation and the stability of aqueous aggregates and aerosols was reported more than a century ago. Many studies have been conducted ever since to characterize the stability, structure, and nucleation barrier of ion-water droplets. Most of these studies have focused on the free-energy surface as a function of cluster size, with an emphasis on the role of ionic charge and radius. This knowledge is fundamental to go beyond the rudimentary ion-induced classical nucleation theory. In the present article, we address this problem from a different perspective, by computing the vapor pressures of (H₂O)_nLi⁺ and (H₂O)_nCl^- aggregates using molecular simulations. Our calculations shed light on the structure, the critical size, the range of stability, and the role of ion-water interactions in aqueous clusters. Moreover, they allow one to assess the accuracy of the classical thermodynamic model, highlighting its strengths and weaknesses.

Ice Nucleation Efficiency of Hydroxylated Organic Surfaces Is Controlled by Their Structural Fluctuations and Mismatch to Ice

Heterogeneous nucleation of ice induced by organic materials is of fundamental importance for climate, biology, and industry. Among organic ice-nucleating surfaces, monolayers of long chain alcohols are particularly effective, while monolayers of fatty acids are significantly less so. As these monolayers expose to water hydroxyl groups with an order that resembles the one in the basal plane of ice, it was proposed that lattice matching between ice and the surface controls their ice-nucleating efficiency. Organic monolayers are soft materials and display significant fluctuations. It has been conjectured that these fluctuations assist in the nucleation of ice. Here we use molecular dynamic simulations and laboratory experiments to investigate the relationship between the structure and fluctuations of hydroxylated organic surfaces and the temperature at which they nucleate ice. We find that these surfaces order interfacial water to form domains with ice-like order that are the birthplace of ice. Both mismatch and fluctuations decrease the size of the preordered domains and monotonously decrease the ice freezing temperature. The simulations indicate that fluctuations depress the freezing efficiency of monolayers of alcohols or acids to half the value predicted from lattice mismatch alone. The model captures the experimental trend in freezing efficiencies as a function of chain length and predicts that alcohols have higher freezing efficiency than acids of the same chain length. These trends are mostly controlled by the modulation of the structural mismatch to ice. We use classical nucleation theory to show that the freezing efficiencies of the monolayers are directly related to their free energy of binding to ice. This study provides a general framework to relate the equilibrium thermodynamics of ice binding to a surface and the nonequilibrium ice freezing temperature and suggests that these could be predicted from the structure of interfacial water.

Molecular mechanism for cavitation in water under tension

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.

Laplace Pressure of Individual H2 Nanobubbles from Pressure-Addition Electrochemistry

The Young-Laplace equation is central to the thermodynamic description of liquids with highly curved interfaces, e.g., nanoscale droplets and their inverse, nanoscale bubbles. The equation relates the pressure difference across an interface to its surface tension and radius of curvature, but the validity in using the macroscopic surface tension for describing curved interfaces with radii smaller than tens of nanometers has been questioned. Here we present electrochemical measurement of Laplace pressures within single H₂ bubbles between 7 and 200 nm radius (corresponding, respectively, to between 200 and 7 atm). Our results demonstrate a linear relationship between a bubble's Laplace pressure and its reciprocal radius, verifying the classical thermodynamic description of H₂ nanobubbles as small as ∼10 nm.

Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics

Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the "mitosis" or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.

Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Surface tension is a macroscopic manifestation of the cohesion of matter, and its value σ_{∞} is readily measured for a flat liquid-vapor interface. For interfaces with a small radius of curvature R, the surface tension might differ from σ_{∞}. The Tolman equation, σ(R)=σ_{∞}/(1+2δ/R), with δ a constant length, is commonly used to describe nanoscale phenomena such as nucleation. Here we report experiments on nucleation of bubbles in ethanol and n-heptane, and their analysis in combination with their counterparts for the nucleation of droplets in supersaturated vapors, and with water data. We show that neither a constant surface tension nor the Tolman equation can consistently describe the data. We also investigate a model including 1/R and 1/R^{2} terms in σ(R). We describe a general procedure to obtain the coefficients of these terms from detailed nucleation experiments. This work explains the conflicting values obtained for the Tolman length in previous analyses, and suggests directions for future work.

Wetting and evaporation of salt-water nanodroplets: A molecular dynamics investigation

We employ molecular dynamics simulations to study the wetting and evaporation of salt-water nanodroplets on platinum surfaces. Our results show that the contact angle of the droplets increases with the salt concentration. To verify this, a second simulation system of a thin salt-water film on a platinum surface is used to calculate the various surface tensions. We find that both the solid-liquid and liquid-vapor surface tensions increase with salt concentration and as a result these cause an increase in the contact angle. However, the evaporation rate of salt-water droplets decreases as the salt concentration increases, due to the hydration of salt ions. When the water molecules have all evaporated from the droplet, two forms of salt crystals are deposited, clump and ringlike, depending on the solid-liquid interaction strength and the evaporation rate. To form salt crystals in a ring, it is crucial that there is a pinned stage in the evaporation process, during which salt ions can move from the center to the rim of the droplets. With a stronger solid-liquid interaction strength, a slower evaporation rate, and a higher salt concentration, a complete salt crystal ring can be deposited on the surface.

Hydrogen-Bond Heterogeneity Boosts Hydrophobicity of Solid Interfaces

Experimental and theoretical studies suggest that the hydrophobicity of chemically heterogeneous surfaces may present important nonlinearities as a function of composition. In this article, this issue is systematically explored using molecular simulations. The hydrophobicity is characterized by computing the contact angle of water on flat interfaces and the desorption pressure of water from cylindrical nanopores. The studied interfaces are binary mixtures of hydrophilic and hydrophobic sites, with and without the ability to form hydrogen bonds with water, intercalated at different scales. Water is described with the mW coarse-grained potential, where hydrogen-bonds are modeled in the absence of explicit hydrogen atoms, via a three-body term that favors tetrahedral coordination. We found that the combination of particles exhibiting the same kind of coordination with water gives rise to a linear dependence of contact angle with respect to composition, in agreement with the Cassie model. However, when only the hydrophilic component can form hydrogen bonds, unprecedented deviations from linearity are observed, increasing the contact angle and the vapor pressure above their values in the purely hydrophobic interface. In particular, the maximum enhancement is seen when a 35% of hydrogen bonding molecules is randomly scattered on a hydrophobic background. This effect is very sensitive to the heterogeneity length-scale, being significantly attenuated when the hydrophilic domains reach a size of 2 nm. The observed behavior may be qualitatively rationalized via a simple modification of the Cassie model, by assuming a different microrugosity for hydrogen bonding and non-hydrogen bonding interfaces.