A perspective on the interfacial properties of nanoscopic liquid drops

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

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.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Probing the Free Energy of Small Water Clusters: Revisiting Classical Nucleation Theory

By addressing the defects in classical nucleation theory (CNT), we develop an approach for extracting the free energy of small water clusters from nucleation rate experiments without any assumptions about the form of the cluster free energy. For temperatures higher than ∼250 K, the extracted free energies from experimental data points indicate that their ratio to the free energies predicted by CNT exhibits nonmonotonic behavior as the cluster size changes. We show that this ratio increases from almost zero for monomers and passes through (at least) one maximum before approaching one for large clusters. For temperatures lower than ∼250 K, the behavior of the ratio between extracted energies and CNT's prediction changes; it increases with cluster size, but it remains below one for almost all of the experimental data points. We also applied a state-of-the-art quantum mechanics model to calculate free energies of water clusters (2-14 molecules); the results support the observed change in behavior based on temperature, albeit for temperatures above and below ∼298 K. We compared two different model chemistries, DLPNO-CCSD(T)/CBS//ωB97xD/6-31++G** and G3, against each other and the experimental value for formation of the water dimer.

The Intrinsic Fragility of the Liquid-Vapor Interface: A Stress Network Perspective

The evolution of the liquid-vapor interface of a Lennard-Jones fluid is examined with molecular dynamics simulations using the intrinsic sampling method. Results suggest clear damping of the intrinsic profiles with increasing temperature. Investigating the surface stress distribution, we have identified a linear variation of the space-filling nature (fractal dimension) of the stress clusters at the intrinsic surface with increasing surface tension or, equivalently, with decreasing temperature. A percolation analysis of these stress networks indicates that the stress field is more disjointed at higher temperatures. This leads to more fragile (or poorly connected) interfaces which result in a reduction in surface tension.

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

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

Mesoscale perspective on the Tolman length

We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension σ as computed from three-dimensional hydrostatic droplets and bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called Tolman length δ. LBM allows one to precisely compute σ at the surface of tension R_{s} and determine the Tolman length from the coefficient of the first order correction. The corresponding values of δ display universality for different equations of state, following a power-law scaling near the critical temperature. The Tolman length has been studied so far mainly via computationally demanding Molecular Dynamics simulations or by means of Density Functional Theory approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.

Cassie State Stability and Gas Restoration Capability of Superhydrophobic Surfaces with Truncated Cone-Shaped Pillars

The gas layer stability on superhydrophobic surfaces and gas restoration on the immersed superhydrophobic surfaces have been great challenges for their practical applications in recent years. Inspired by the naturally existing mushroom-like super-repellent superhydrophobic patterns, we choose superhydrophobic surfaces with truncated cone-shaped pillars as our research objects to tackle such challenges by tuning their geometrical parameters. We perform molecular dynamics simulations to investigate the Cassie-Wenzel transition under external pressure and the Wenzel-Cassie transition due to underwater spreading of compressed bubbles. Theories based on the Young-Laplace equation and total free-energy variation are developed to explore the influence of geometrical parameters of pillars on the pressure resistance and underwater gas restoration, which is in good agreement with simulation results. These simulation results and theoretical analysis suggest that cork-shaped pillars, analogous to the surface structures of natural organisms like springtails and Salvinia leaves, can be super-repellent to the liquid and favorable for the gas spreading process. Our study provides theoretical guidance for the design of superhydrophobic surfaces with both Cassie state stability and gas restoration capability.

Structure and Contact Angle in Sessile Droplets of Binary Mixtures of Lennard-Jones Chains: A Molecular Dynamics Study

Molecular dynamics simulations were carried out to investigate cylindrical droplets consisting of binary mixtures of Lennard-Jones (LJ) fluids in contact with a solid substrate. The droplets are composed of mixtures of the monomeric LJ fluid plus linear-tangent chains of 2, 10, 20, and 30 segments per chain that interact through a harmonic potential and the spherically truncated and shifted potential Lennard-Jones. The solid surface was modeled as a semi-infinite platinum substrate with an FCC structure that interacts with the fluid by means of a LJ 9-3 potential. We place emphasis on the effect of mixing a monomeric LJ fluid with heavy components on the contact angle and on the droplet structure, especially in the liquid-solid region. The density profiles of the droplets reveal a strong discrete layering of the fluid in the vicinity of the solid-liquid interface. The layering is more pronounced at low temperatures and for mixtures of short chains (symmetric mixtures). The ordering of the fluid was much less intense for fluids of long chains (asymmetric mixtures), and some cases even show gas enrichment at the solid-liquid interface. Enrichment at the vapor-liquid interfaces and density inversion can also be observed. However, these effects are not as marked as in planar interfaces. The contact angle between the droplet and the substrate is calculated by fitting an ellipse to the vapor-liquid interface defined by the Gibbs dividing surface. In general, an increment in the concentration of the heavy component and a reduction of the temperature resulted in an increase of the contact angle, which in turn disfavored the wetting of the droplet.

Capillary condensation under atomic-scale confinement

Capillary condensation of water is ubiquitous in nature and technology. It routinely occurs in granular and porous media, can strongly alter such properties as adhesion, lubrication, friction and corrosion, and is important in many processes used by microelectronics, pharmaceutical, food and other industries^1-4. The century-old Kelvin equation⁵ is frequently used to describe condensation phenomena and has been shown to hold well for liquid menisci with diameters as small as several nanometres^1-4,6-14. For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules^1-22. Here we use van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation within them. Our smallest capillaries are less than four ångströms in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, we find that the macroscopic Kelvin equation using the characteristics of bulk water describes the condensation transition accurately in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphite) ones. We show that this agreement is fortuitous and can be attributed to elastic deformation of capillary walls^23-25, which suppresses the giant oscillatory behaviour expected from the commensurability between the atomic-scale capillaries and water molecules^20,21. Our work provides a basis for an improved understanding of capillary effects at the smallest scale possible, which is important in many realistic situations.

Equivalence between condensation and boiling in a Lennard-Jones fluid

Condensation and boiling are phase transitions highly relevant to industry, geology, and atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid, respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard-Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.

Hydrodynamics across a fluctuating interface

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics, we can pick apart the interface structure and understand surface tension. In this work, we derive an exact mechanical formulation of hydrodynamics for a liquid-vapor interface using a control volume, which moves with the surface. This mathematical framework provides the local definition of hydrodynamic fluxes at any point on the surface. These are represented not only by the flux of molecules and intermolecular interactions acting across the surface but also as a result of the instantaneous local curvature and movement of the surface itself. By explicitly including the surface dynamics in the equations of motion, we demonstrate an exact balance between kinetic and configurational pressure normal to the surface. The hydrodynamic analysis makes no assumptions regarding the probability distribution function, so it is valid for any system arbitrarily far from thermodynamic equilibrium. The presented equations provide a theoretical basis for the study of time-evolving interface phenomena, such as bubble nucleation, droplet dynamics, and liquid-vapor instabilities.

Learning Coarse-Grained Potentials for Binary Fluids

For a multiple-fluid system, CG models capable of accurately predicting the interfacial properties as a function of curvature are still lacking. In this work, we propose a new probabilistic machine learning (ML) model for learning CG potentials for binary fluids. The water-hexane mixture is selected as a typical immiscible binary liquid-liquid system. We develop a new CG force field (FF) using the Shinoda-DeVane-Klein (SDK) FF framework and compute parameters in this CG FF using the proposed probabilistic ML method. It is shown that a standard response-surface approach does not provide a unique set of parameters, as it results in a loss function with multiple shallow minima. To address this challenge, we develop a probabilistic ML approach where we compute the probability density function (PDF) of parameters that minimize the loss function. The PDF has a well-defined peak corresponding to a unique set of parameters in the CG FF that reproduces the desired properties of a liquid-liquid interface. We compare the performance of the new CG FF with several existing FFs for the water-hexane mixture, including two atomistic and three CG FFs with respect to modeling the interface structure and thermodynamic properties. It is demonstrated that the new FF significantly improves the CG model prediction of both the interfacial tension and structure for the water-hexane mixture.

Interfacial free energy of a liquid-solid interface: Its change with curvature

We analyze the changes in the interfacial free energy between a spherical solid cluster and a fluid due to the change of the radius of the solid. Interfacial free energies from nucleation studies using the seeding technique for four different systems, being hard spheres, Lennard-Jones, and two models of water (mW and TIP4P/ICE), were plotted as a function of the inverse of the radius of the solid cluster. In all cases, the interfacial free energy was a linear function of the inverse of the radius of the solid cluster and this is consistent with Tolman's equation. This linear behavior is shown not only in isotherms but also along isobars. The effect of curvature on the interfacial free energy is more pronounced in water, followed by hard spheres, and smaller for Lennard-Jones particles. We show that it is possible to estimate nucleation rates of Lennard-Jones particles at different pressures by using information from simple NpT simulations and taking into account the variation of the interfacial free energy with the radius of the solid cluster. Neglecting the effects of the radius on the interfacial free energy (capillarity approximation) leads to incorrect values of the nucleation rate. For the Lennard-Jones system, the homogeneous nucleation curve is not parallel to the melting curve as was found for water in previous work. This is due to the increase in the interfacial free energy along the coexistence curve as the pressure increases. This work presents a simple and relatively straightforward way to approximately estimate nucleation rates.

Studying vapor-liquid transition using a generalized ensemble

Homogeneous vapor-liquid nucleation is studied using the generalized Replica Exchange Method (gREM). The generalized ensemble allows the study of unstable states that cannot directly be studied in the canonical ensemble. Along with replica exchange, this allows for efficient sampling of the multiple states in a single simulation. Statistical Temperature Weighted Histogram Analysis Method is used for postprocessing to get a continuous free energy curve from bulk vapor to bulk liquid. gREM allows the study of planar, cylindrical, and spherical interfaces in a single simulation. The excess Gibbs free energy for the formation of a spherical liquid droplet in vapor for a Lennard-Jones system is calculated from the free energy curve and compared against the umbrella sampling results. The nucleation free energy barrier obtained from gREM is then used to calculate the nucleation rate without relying on any classification scheme for separating the vapor and liquid.

Interfaces of Gas-Aerosol Particles: Relative Humidity and Salt Concentration Effects

The growth of aerosol particles is intimately related to chemical reactions in the gas phase and particle phase and at gas-aerosol particle interfaces. While chemical reactions in gas and particle phases are well documented, there is very little information regarding interface-related reactions. The interface of gas-aerosol particles not only facilitates a physical channel for organic species to enter and exit but also provides a necessary lane for culturing chemical reactions. The physical and chemical properties of gas-particle interfaces have not been studied extensively, nor have the reactions occurring at the interfaces been well researched. This is mainly due to the fact that there is a lack of suitable in situ interface-sensitive analytical techniques for direct measurements of interfacial properties. The motivation behind this research is to understand how interfaces play a role in the growth of aerosol particles. We have developed in situ interface-specific second harmonic scattering to examine interfacial behaviors of molecules of aerosol particles under different relative humidity (RH) and salt concentrations. Both the relative humidity and salt concentration can change the particle size and the phase of the aerosol. RH not only varies the concentration of solutes inside aerosol particles but also changes interfacial hydration in local regions. Organic molecules were found to exhibit distinct behaviors at the interfaces and bulk on NaCl particles under different RH levels. Our quantitative analyses showed that the interfacial adsorption free energies remain unchanged while interfacial areas increase as the relative humidity increases. Furthermore, the surface tension of NaCl particles decreases as the RH increases. Our experimental findings from the novel nonlinear optical scattering technique stress the importance of interfacial water behaviors on aerosol particles in the atmosphere.

Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale for Enhanced Gas Recovery from Density Functional Theory

CO₂ competitive sorption with shale gas under various conditions from simple to complex pore characteristics is studied using a molecular density functional theory (DFT) that reduces to perturbed chain-statistical associating fluid theory in the bulk fluid region. The DFT model is first verified by grand canonical Monte Carlo simulation in graphite slit pores for pure and binary component systems at different temperatures, pressures, pore sizes, and bulk gas compositions for methane/ethane with CO₂. Then, the model is utilized in multicomponent systems that include CH₄, C₂H₆, and C3+ components of different compositions. It is shown that the selectivity of CO₂ decreases with increases in temperature, pressure, nanopore size, and average molecular weight of shale gas. Extending the model to more realistic situations, we consider the impact of water present in the pore and consider the effect of permeation of fluid molecules into the kerogen that forms the pore walls. The water-graphite interaction is calibrated with contact angle from molecular simulation data from the literature. The kerogen pore model prediction of gas absolute sorption is compared with experimental and molecular simulation values in the literature. It is shown that the presence of water reduces the CO₂ adsorption but improves the CO₂ selectivity. The dissolution of gases into the kerogen matrix also leads to the increase in CO₂ selectivity. The effect of kerogen type and maturity on the gas sorption amount and CO₂ selectivity is also studied. The associated mechanisms are discussed to provide fundamental understanding for gas recovery by CO₂.

Measurement of the Curvature-Dependent Surface Tension in Nucleating Colloidal Liquids

The curvature dependence of the surface tension is central to the nucleation of liquids, but remains difficult to access experimentally and predict theoretically. This curvature dependence arises from the curvature-dependent molecular structure, which, for small nuclei, can deviate significantly from that of the planar liquid interface. Simulations and density functional theory have been used to predict this curvature dependence, however with contradicting results. Here, we provide the first direct measurement of the curvature-dependent surface tension in nucleating colloidal liquids. We employ critical Casimir forces to finely adjust colloidal particle interactions and induce liquid nucleation, and image individual nuclei at the particle scale to measure their curvature-dependent surface tension directly from thermally excited surface distortions. Using continuum models, we elucidate the interplay between nucleus structure, particle pair potential, and surface tension. Our results reveal a 20% lower surface tension for nuclei of critical size compared to bulk liquids, leading to 3 orders of magnitude higher nucleation rates, thus highlighting the importance of surface tension curvature corrections for accurate prediction of nucleation rates.

Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

The curvature dependence of the surface tension can be described by the Tolman length (first-order correction) and the rigidity constants (second-order corrections) through the Helfrich expansion. We present and explain the general theory for this dependence for multicomponent fluids and calculate the Tolman length and rigidity constants for a hexane-heptane mixture by use of square gradient theory. We show that the Tolman length of multicomponent fluids is independent of the choice of dividing surface and present simple formulae that capture the change in the rigidity constants for different choices of dividing surface. For multicomponent fluids, the Tolman length, the rigidity constants, and the accuracy of the Helfrich expansion depend on the choice of path in composition and pressure space along which droplets and bubbles are considered. For the hexane-heptane mixture, we find that the most accurate choice of path is the direction of constant liquid-phase composition. For this path, the Tolman length and rigidity constants are nearly linear in the mole fraction of the liquid phase, and the Helfrich expansion represents the surface tension of hexane-heptane droplets and bubbles within 0.1% down to radii of 3 nm. The presented framework is applicable to a wide range of fluid mixtures and can be used to accurately represent the surface tension of nanoscopic bubbles and droplets.

Importance of the tail corrections on surface tension of curved liquid-vapor interfaces

We report molecular simulations of the liquid-vapor cylindrical interface of methane. We apply the truncated Lennard-Jones potential and specific long-range corrections for the surface tension developed especially for cylindrical interfaces. We investigate the impact of the cutoff on the radial density profile, the intrinsic and long-range correction parts to the surface tension, and Tolman length. We also study the curvature dependence of the surface tension as a function of the cutoff used. In this work we shed light that both density and Tolman length are cutoff-dependent whereas the total surface tension is slightly curvature and cutoff dependent.

Free-energy barriers for crystal nucleation from fluid phases

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows us to extract the surface free energy of the nucleus. Neither the knowledge of the (in general nonspherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of 0.15, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as ΔF^{*}=(4π/3)^{1/3}γ[over ¯](V^{*})^{2/3}+const with the nucleus volume V^{*}, and the effective surface tension γ[over ¯] that accounts implicitly for the nonspherical shape can be precisely estimated.

Changes in Surface Tension of Aqueous Humor in Anterior Segment Ocular Pathologies

The aim of this study was to identify and determine differences in surface tension (ST) of aqueous humor (AH) in patients with cataract, glaucoma and Fuchs endothelial dystrophy (FED). Two hundred and two samples of AH were analyzed (control n = 22; cataract n = 56; glaucoma n = 81; and n = FED 43). Patients with previous history of anterior segment surgery, anterior segment pathology or intraocular injections were excluded from the study. Different types of glaucoma were identified, cataracts were graded using total phaco time data during surgery and clinical severity of FED was assessed by clinical examination. Around 150 microliters AH were obtained during the first step of a surgical procedure, lensectomy, phacoemulsification, nonpenetrating deep sclerotomy (NPDE) and Descemet membrane endothelial keratoplasty (DMEK). A pendant drop-based optical goniometer OCA-15 (Dataphysics, Filderstadt, Germany) was used to measure surface tension. Mean ST was 65.74 ± 3.76 mN/m, 63.59 ± 5.50 mN/m, 64.35 ± 6.99 mN/m, and 60.89 ± 3.73 mN/m in control, cataract, glaucoma and FED patients respectively. Statistically significant differences between FED and control group were found (p < 0.001). Lens condition, cataract maturity, age, and gender did not show influence in ST. ST of AH is significantly decreased in FED patients independently from age and lens condition. These findings may aid to the understanding of the physiopathology of the disease.

Interactions between Phospholipids and Organic Phases: Insights into Lipoproteins and Nanoemulsions

The adsorption of phosphatidylcholines (PCs), dissolved in squalene or squalane as an organic phase, was studied at the interface with water. Using profile analysis tensiometry, the equilibrium adsorption isotherms, minimum molecular interfacial areas, and solubility limits were derived. For squalene, differences in PC solubility and interfacial adsorption were found, depending on PC saturation. Compared to saturated PCs, unsaturated PCs showed a 3-fold-lower interfacial density but up to a 28-fold-higher critical aggregation concentration (CAC). In addition, the solubility limit of unsaturated PC in squalene and in its saturated form squalane diverged by a factor of 739. These findings provided evidence for steric repulsion or π-π interactions of π bonds in both solvent and solute or both effects acting complementarily. In squalane, low solubilities but high interfacial densities were found for all investigated PCs. Changes in fatty acid chain lengths showed that the influence of the increases in entropy and enthalpy on solubility is much smaller than solvent/solute interactions. Oxidation products of squalene lowered the interfacial tension, but increasing concentrations of PC expelled them from the interface. The CAC of saturated PC was increased by oxidation products of squalene whereas that of unsaturated PCs was not. Our findings indicate that the oxidation of triglycerides in lipoprotein cores can lead to increased solubility of saturated phospholipids covering the lipoproteins, contributing to destabilization, coalescence, and terminally the formation of atherosclerotic plaques. The consideration of solvent/solute interactions in molecular modeling may contribute to the interfacial tension and the corresponding kinetic or thermodynamic stability of lipoproteins. Measured areas per molecule prove that PCs form monolayers of different interfacial densities at the squalene/water interface but multilayers at the squalane/water interface. These findings showed that combinations of solvent or solute saturation affect the outcome for nanoemulsions forming either expanded or condensed monolayers or multilayers.

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.

Nanothermodynamics of large iron clusters by means of a flat histogram Monte Carlo method

The thermodynamics of iron clusters of various sizes, from 76 to 2452 atoms, typical of the catalyst particles used for carbon nanotubes growth, has been explored by a flat histogram Monte Carlo (MC) algorithm (called the σ-mapping), developed by Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. This method provides the classical density of states, gp(Ep) in the configurational space, in terms of the potential energy of the system, with good and well controlled convergence properties, particularly in the melting phase transition zone which is of interest in this work. To describe the system, an iron potential has been implemented, called "corrected EAM" (cEAM), which approximates the MEAM potential of Lee et al. [Phys. Rev. B 64, 184102 (2001)] with an accuracy better than 3 meV/at, and a five times larger computational speed. The main simplification concerns the angular dependence of the potential, with a small impact on accuracy, while the screening coefficients S(ij) are exactly computed with a fast algorithm. With this potential, ergodic explorations of the clusters can be performed efficiently in a reasonable computing time, at least in the upper half of the solid zone and above. Problems of ergodicity exist in the lower half of the solid zone but routes to overcome them are discussed. The solid-liquid (melting) phase transition temperature T(m) is plotted in terms of the cluster atom number N(at). The standard N(at)(-1/3) linear dependence (Pawlow law) is observed for N(at) >300, allowing an extrapolation up to the bulk metal at 1940 ±50 K. For N(at) <150, a strong divergence is observed compared to the Pawlow law. The melting transition, which begins at the surface, is stated by a Lindemann-Berry index and an atomic density analysis. Several new features are obtained for the thermodynamics of cEAM clusters, compared to the Rydberg pair potential clusters studied in Paper I.