Gibbsian Surface Thermodynamics

Stability Analysis of a Multicomponent Vapor-Gas Bubble in Contact with a Liquid-Gas Solution

Stability of vapor-gas bubbles, homogeneously nucleated within a liquid-gas solution, depends on the temperature and pressure of the liquid phase, along with the concentration of dissolved gaseous components. While extensive theoretical and experimental investigations have been conducted on bubble nucleation within single-component systems, research on multicomponent systems has mainly focused on binary liquid-gas solutions comprising a solvent and one dissolved gas. Moreover, existing studies on the stability of vapor-gas bubbles have predominantly examined the stability with respect to bubble size, leaving other critical factors relatively unexplored. Here, we present a methodology to determine potential equilibrium states for a single vapor-gas bubble homogeneously nucleated within a large multicomponent liquid-gas solution, encompassing a subcritical solvent and n - 1 gaseous components, with temperature and liquid phase pressure held constant. Additionally, we assess equilibrium state stability by analyzing the free energy change of the system with respect to both bubble size and the composition of the vapor-gas phase within the bubble, using rigorous phase equilibrium equations to account for nonideal behavior in both liquid-gas and vapor-gas phases. We then apply this to investigate the number and nature of equilibrium states in a ternary system of water-oxygen-nitrogen across various scenarios of oxygen and nitrogen saturation levels in the liquid phase, while also meticulously examining the effects of liquid phase temperature and pressure on the stability of the system. The proposed model can be used to optimize the design of micro-nano bubble technologies for diverse engineering applications, ranging from agriculture to water treatment and biomedicine.

Gibbsian surface thermodynamic analysis of emulsion liquid membranes

The emulsion liquid membrane is a promising technique for separating pollutants such as metals, weak acids and bases, mineral species, hydrocarbons, and biological substances. The popularity of the membrane process is due to its high mass transfer efficiency, process simplicity, and low energy consumption. Despite significant advancements in the field of emulsion liquid membranes, the effect of the interfacial curvature on component distribution remains largely uninvestigated. In the present study, considering the emulsion liquid membrane where no reaction takes place, the thermodynamic equilibrium relationships are calculated while considering the effect of interfacial curvature between the phases. The Gibbsian surface thermodynamic method is employed to derive the equations at equilibrium for the composite system of emulsion liquid membrane. With the obtained equations, the mole fraction and percentage extraction of the desired substance can be calculated under various conditions, such as different surfactant concentration, and droplet size, as well as assuming ideal or non-ideal condition for the solution. The results indicate that by reducing the size of internal droplets to the nanoscale, the effect of interfacial curvature becomes significant, and the extraction percentage gets higher.

Predictive Thermodynamics for Isochoric (Constant-Volume) Cryopreservation Systems

Cryopreservation is the preservation and storage of biomaterials using low temperatures. There are several approaches to cryopreservation, and these often include the use of cryoprotectants, which are solutes used to lower the freezing point of water. Isochoric (constant-volume) cryopreservation is a form of cryopreservation that has been gaining interest over the past 18 years. This method utilizes the anomalous nature of water in that it expands as it freezes. The expansion of ice on freezing is used to induce a pressure in the system that limits ice growth. In this work, we use Gibbsian thermodynamics, the Elliott et al. multisolute osmotic virial equation, the Feistel and Wagner correlation for ice Ih, and the Grenke and Elliott correlation for the thermodynamic properties of liquid water at low temperatures and high pressures to predict how the pressure, volume fraction of ice, and solute concentration in the unfrozen fraction change as the solution is cooled isochorically. We then verified our model by predicting experimental results for saline solutions and ternary aqueous solutions containing NaCl and organic compounds commonly used as cryoprotectants: glycerol, ethylene glycol, propylene glycol, and dimethyl sulfoxide. We found that our model accurately predicts experimental data that were collected for cryoprotectant concentrations as high as 5 M, and temperatures as low as -25 °C. Since we have shown that our liquid water correlation, on which this work was based, makes accurate predictions to -70 °C, as long as the pressure is not higher than 400 MPa, we anticipate that the prediction methods presented in this work will be accurate down to -70 °C. In this work we also modeled how sealing the isochoric chamber at room temperature versus at the nucleation temperature impacts isochoric freezing. The prediction methods developed in this work can be used in the future design of isochoric cryopreservation experiments and protocols.

The Role of Geometry on the Ease of Solidification Inside and Out of Cylindrical Nanopores

We investigated the role of a nanoporous particle on the formation of macroscopic solid in the framework of equilibrium thermodynamics and from the free-energy perspective. The model particle has cylindrical pores with equidistant circular openings on the particle surface. We focused on two potentially limiting steps: (i) the solid nucleation from liquid inside a single pore and (ii) the bridging of multiple pores on the particle surface. We examined the nucleation near the liquid-vapor meniscus inside a pore by considering different solid-vapor and solid-pore wall contact angles, as well as the liquid-vapor meniscus angles. For bridging, we quantified the effects of the proximity of neighboring pores and the number of participating pores where we considered two or three pores, placed two different distances apart, and three contact angles of the solid with the particle surface. Except in special cases where an analytical solution could be developed, we determined the equilibrium nucleus and bridge shapes numerically using the Surface Evolver code. The geometry of these equilibrium shapes was the key for correctly calculating the energy barriers. Our results indicate that the meniscus angle can be an important factor in reducing the barrier for nucleation if the internal angles of the solid nucleus satisfy a certain criterion. For the solid growth out of the pores, we found that the barriers were significantly lower in the presence of multiple, closely packed pores compared to the growth from a single pore. This paper is deliberately written with no reference to material properties or a specific process to highlight the generality of geometry-controlled barriers. A direct application where our findings can be particularly valuable is the ice formation in clouds, which is the subject of intensive research in atmospheric sciences for its role in influencing precipitation patterns and hence the climate.

Oiling-Out: Insights from Gibbsian Surface Thermodynamics by Stability Analysis

The crystallization process is a significant stage in the pharmaceutical industry. During the process of crystallization with cooling, it is possible for a secondary liquid phase to appear before the formation of crystals. This phenomenon is called "oiling out" or liquid-liquid phase separation (LLPS). In this article, we explore the oiling-out phenomenon in a binary system of water and vanillin using stability analysis based on Gibbsian surface thermodynamics. To obtain the full picture of oiling out, we investigated three cases: droplet-solute-lean liquid equilibrium (DLE), crystal-solute-rich liquid equilibrium (CL'E), and crystal-solute-lean liquid equilibrium (CLE). The phase diagram of the system is plotted using the NRTL model for activity coefficients, along with considering the effect of the interfacial curvature on the phase diagram. From the phase boundaries and free-energy diagram of each case, we showed that the occurrence of the oiling-out phenomenon is justified based on the lower energy barrier of the droplet formation compared to that of the crystal formation. However, the energy level of a stable crystal is significantly lower and hence more stable than that of a stable droplet. Finally, we have determined different regions for droplet and crystal formation in the metastable phase diagram based on their supersaturation and provide insight for the oiling-out phenomenon.

Predicting freezing points of ternary salt solutions with the multisolute osmotic virial equation

Previously, the multisolute osmotic virial equation with the combining rules of Elliott et al. has been shown to make accurate predictions for multisolute solutions with only single-solute osmotic virial coefficients as inputs. The original combining rules take the form of an arithmetic average for the second-order mixed coefficients and a geometric average for the third-order mixed coefficients. Recently, we derived generalized combining rules from a first principles solution theory, where all mixed coefficients could be expressed as arithmetic averages of suitable binary coefficients. In this work, we empirically extended the new model to account for electrolyte effects, including solute dissociation, and demonstrated its usefulness for calculating the properties of multielectrolyte solutions. First, the osmotic virial coefficients of 31 common salts in water were tabulated based on the available freezing point depression (FPD) data. This was achieved by polynomial fitting, where the degree of the polynomial was determined using a special criterion that accounts for the confidence intervals of the coefficients. Then, the multisolute model was used to predict the FPD of 11 ternary electrolyte solutions. Furthermore, models with the new combining rules and the original combining rules of Elliott et al. were compared using both mole fraction and molality as concentration units. We find that the mole-fraction-based model with the new combining rules performs the best and that the results agree well with independent experimental measurements with an all-system root-mean-square error of 0.24 osmoles/kg (0.45 °C) and close to zero mean bias for the entire dataset (371 data points).

Multicomponent solutions: Combining rules for multisolute osmotic virial coefficients

This paper presents an exploration of a specific type of a generalized multicomponent solution model, which appears to be first given by Saulov in the current explicit form. The assumptions of the underlying theory and a brief derivation of the main equation have been provided preliminarily for completeness and notational consistency. The resulting formulae for the Gibbs free energy of mixing and the chemical potentials are multivariate polynomials with physically meaningful coefficients and the mole fractions of the components as variables. With one additional assumption about the relative magnitudes of the solvent-solute and solute-solute interaction exchange energies, combining rules were obtained that express the mixed coefficients of the polynomial in terms of its pure coefficients. This was done by exploiting the mathematical structure of the asymmetric form of the solvent chemical potential equation. The combining rules allow one to calculate the thermodynamic properties of the solvent with multiple solutes from binary mixture data only (i.e., each solute with the solvent), and hence, are of practical importance. Furthermore, a connection was established between the osmotic virial coefficients derived in this work and the original osmotic virial coefficients of Hill found by employing a different procedure, illustrating the equivalency of what appears to be two different theories. A validation of the combining rules derived here has been provided in a separate paper where they were successfully used to predict the freezing points of ternary salt solutions of water.

Additives in Nanocrystalline Tin Dioxide: Recent Progress in the Characterization of Materials for Gas Sensor Applications

Tin dioxide has huge potential and is widely studied and used in different fields, including as a sensitive material in semiconductor gas sensors. The specificity of the chemical activity of tin dioxide in its interaction with the gas phase is achieved via the immobilization of various modifiers on the SnO2 surface. The type of additive, its concentration, and the distribution between the surface and the volume of SnO2 crystallites have a significant effect on semiconductor gas sensor characteristics, namely sensitivity and selectivity. This review discusses the recent approaches to analyzing the composition of SnO2-based nanocomposites (the gross quantitative elemental composition, phase composition, surface composition, electronic state of additives, and mutual distribution of the components) and systematizes experimental data obtained using a set of analytical methods for studying the concentration of additives on the surface and in the volume of SnO2 nanocrystals. The benefits and drawbacks of new approaches to the high-accuracy analysis of SnO2-based nanocomposites by ICP MS and TXRF methods are discussed.

Thiocyanate-Stabilized Pseudo-cubic Perovskite CH(NH2)2PbI3 from Coincident Columnar Defect Lattices

α-FAPbI3 (FA+ = CH(NH2)2+) with a cubic perovskite structure is promising for photophysical applications. However, α-FAPbI3 is metastable at room temperature, and it transforms to the δ-phase at a certain period of time at room temperature. Herein, we report a thiocyanate-stabilized pseudo-cubic perovskite FAPbI3 with ordered columnar defects (α'-phase). This compound has a √5ap × √5ap × ap tetragonal unit cell (ap: cell parameter of primitive perovskite cell) with a band gap of 1.91 eV. It is stable at room temperature in a dry atmosphere. Furthermore, the presence of the α'-phase in a mixed sample with the δ-phase drastically reduces the δ-to-α transition temperature measured on heating, suggesting the reduction of the nucleation energy of the α-phase or thermodynamic stabilization of the α-phase through epitaxy. The defect-ordered pattern in the α'-phase forms a coincidence-site lattice at the twinned boundary of the single crystals, thus hinting at an epitaxy- or strain-based mechanism of α-phase formation and/or stabilization. In this study, we developed a new strategy to control defects in halide perovskites and provided new insight into the stabilization of α-FAPbI3 by pseudo-halide and grain boundary engineering.

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.

Quantification of Surface Tension Effects and Nucleation-and-Growth Rates during Self-Assembly of Biological Condensates

Liquid-solid and liquid-liquid phase separation (PS) drives the formation of functional and disease-associated biological assemblies. Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a limited number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. The exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.

Surface tension models for binary aqueous solutions: a review and intercomparison

The liquid-air surface tension of aqueous solutions is a fundamental quantity in multi-phase thermodynamics and fluid dynamics and thus relevant in many scientific and engineering fields. Various models have been proposed for its quantitative description. This Perspective gives an overview of the most popular models and their ability to reproduce experimental data of ten binary aqueous solutions of electrolytes and organic molecules chosen to be representative of different solute types. In addition, we propose a new model which reproduces sigmoidal curve shapes (Sigmoid model) to empirically fit experimental surface tension data. The surface tension of weakly surface-active substances is well reproduced by all models. In contrast, only few models successfully model the surface tension of aqueous solutions with strongly surface-active substances. For substances with a solubility limit, usually no experimental data is available for the surface tension of supersaturated solutions and the pure liquid solute. We discuss ways in which these can be estimated and emphasize the need for further research. The newly developed Sigmoid model best reproduces the surface tension of all tested solutions and can be recommended as a model for a broad range of binary mixtures and over the entire concentration range.

A simple theory for interfacial properties of dilute solutions

Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid–vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work, we relate the interfacial properties of dilute multicomponent solutions to the interactions between solutes. We first derive a simple model for the surface excess of solutes in terms of thermodynamic observables. We then develop a lattice-based statistical mechanical perturbation theory to derive these observables from microscopic interactions. Rather than adopting a random mixing approximation, this dilute solution theory (DST) exactly treats solute–solute interactions to lowest order in perturbation theory. Although it cannot treat concentrated solutions, Monte Carlo (MC) simulations demonstrate that DST describes the interactions in dilute solutions with much greater accuracy than regular solution theory. Importantly, DST emphasizes a fundamental distinction between the “intrinsic” and “effective” preferences of solutes for interfaces. DST predicts that three classes of solutes can be distinguished by their intrinsic preference for interfaces. While the surface preference of strong depletants is relatively insensitive to interactions, the surface preference of strong surfactants can be modulated by interactions at the interface. Moreover, DST predicts that the surface preference of weak depletants and weak surfactants can be qualitatively inverted by interactions in the bulk. We also demonstrate that DST can be extended to treat surface polarization effects and to model experimental data. MC simulations validate the accuracy of DST predictions for lattice systems that correspond to molar concentrations.

Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Disjoining Pressure of Water in Nanochannels

The disjoining pressure of water was estimated from wicking experiments in 1D silicon dioxide nanochannels of heights of 59, 87, 124, and 1015 nm. The disjoining pressure was found to be as high as ∼1.5 MPa while exponentially decreasing with increasing channel height. Such a relation resulting from the curve fitting of experimentally derived data was implemented and validated in computational fluid dynamics. The implementation was then used to simulate bubble nucleation in a water-filled 59 nm nanochannel to determine the nucleation temperature. Simultaneously, experiments were conducted by nucleating a bubble in a similar 58 nm nanochannel by laser heating. The measured nucleation temperature was found to be in excellent agreement with the simulation, thus independently validating the disjoining pressure relation developed in this work. The methodology implemented here integrates experimental nanoscale physics into continuum simulations thus enabling numerical study of various phenomena where disjoining pressure plays an important role.

Thermodynamic Investigation of Droplet-Droplet and Bubble-Droplet Equilibrium in an Immiscible Medium

In the absence of external fields, interfacial tensions between different phases dictate the equilibrium morphology of a multiphase system. Depending on the relative magnitudes of these interfacial tensions, a composite system made up of immiscible fluids in contact with one another can exhibit contrasting behavior: the formation of lenses in one case and complete encapsulation in another. Relatively simple concepts such as the spreading coefficient (SC) have been extensively used by many researchers to make predictions. However, these qualitative methods are limited to determining the nature of the equilibrium states and do not provide enough information to calculate the exact equilibrium geometries. Moreover, due to the assumptions made, their validity is questionable at smaller scales where pressure forces due to curvature of the interfaces become significant or in systems where a compressible gas phase is present. Here we investigate equilibrium configurations of two fluid drops suspended in another fluid, which can be seen as a simple building block of more complicated systems. We use Gibbsian composite-system thermodynamics to derive equilibrium conditions and the equation acting as the free energy (thermodynamic potential) for this system. These equations are then numerically solved for an example system consisting of a dodecane drop and an air bubble surrounded by water, and the relative stability of distinct equilibrium shapes is investigated based on free-energy comparisons. Quantitative effects of system parameters such as interfacial tensions, volumes, and the scale of the system on geometry and stability are further explored. Multiphase systems similar to the ones analyzed here have broad applications in microfluidics, atmospheric physics, soft photonics, froth flotation, oil recovery, and some biological phenomena.

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.