The liquid–gas interface of oxygen–nitrogen solutions 2: Description in the Framework of the van der Waals gradient theory

The van der Waals gradient theory (vdW GT) is used to calculate surface tension, density profiles, adsorption, the Tolman length and to determine the position of dividing surfaces in the liquid–gas interface of an oxygen–nitrogen solution. The Helmholtz energy density (HED) is determined via an equation of state (EOS), unified for a liquid and gas, which describes stable, metastable and two-phase states of solutions. The influence parameters are calculated from data on the surface tension of pure components with the use of the mixing rule. At temperatures T > 100 K the vdW GT describes experimental data on the surface tension of oxygen–nitrogen solutions [V.G. Baidakov, A.M. Kaverin, V.N. Andbaeva, The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension, Fluid Phase Equilib. 270 (2008) 116–120] within the experimental error. It is shown that the Tolman length, which determines the dependence of surface tension on the curvature of the dividing surface, depends considerably on the solution concentration.     

On the thermodynamics of particle-stabilized emulsions: curvature effects and catastrophic phase inversion

The flexural properties of a particle adsorption monolayer are investigated theoretically. If the particles are not densely packed, the interfacial bending moment and the spontaneous curvature (due to the particles) are equal to zero. The situation changes if the particles are closely packed. Then the particle adsorption monolayer possesses a significant bending moment, and the interfacial energies of bending and dilatation become comparable. In this case, the bending energy can either stabilize or destabilize the Pickering emulsion, depending on whether the particle contact angle is smaller or greater than 90 degrees . Theoretical expressions are derived for the bending moment, for the curvature elastic modulus, and for the work of interfacial deformation and emulsification. The latter is dominated by the work for creation of a new oil-water interface and by the work for particle adsorption. The curvature effects give a contribution of second order, which is significant only for emulsification at 50:50 water/oil volume fractions. A thermodynamic criterion for the type of the formed emulsion is proposed. It predicts the existence of a catastrophic phase inversion in particle-stabilized emulsions, in agreement with the experimental observations. The derived theoretical expressions could find application for interpretation of experimental data on production and stability of Pickering emulsions.     

Simulating the effect of surfactant structure on bending moduli of monolayers

We have used dissipative particle dynamics to simulate amphiphilic monolayers on the interface between oil and water. An ultralow interfacial tension is imposed by means of Monte Carlo to resemble the amphiphilic films that separate oil and water regions in microemulsions. We calculate the bending modulus by analyzing the undulation spectrum. By varying the surfactant chain length and topology we investigate the effect of surfactant structure and composition of the monolayer on the bending moduli. We find that increasing the thickness has a larger effect than increasing the density of the layer. This follows from the observations that at a given interfacial tension, the bending modulus increases with chain length and is larger for linear than branched surfactants. The increase with chain length is approximately linear, which is slower than the theoretical predictions at a fixed area. We also investigated a binary mixture of short and long surfactants compared to pure layers of the same average chain length. We find a roughly linear decrease in bending modulus with mole fraction of short surfactants. Furthermore, the mixed film has a lower bending modulus than the corresponding pure film for all mole fractions. Linking the bending moduli to the structure of the surfactants is an important step in predicting the stability of microemulsions.     

Vinyl acetate emulsion polymerization. I. Effect of ionic strength and temperature on monomer solubility in the ionically stabilized polymer particle

Solubility of monomer in the polymer was strongly affected by ionic strength; with increasing ionic strength, solubility was found to increase. At constant temperature, this was entirely due to the decrease in interfacial tension, as the condensation of surfactant proceeded at the interface. The temperature affected both the polymer–solvent interaction parameter as well as the interfacial tension. These are the two parameters on which solubility depends. The variations of interfacial tension with temperature was found to be complex, but entirely dependent on the entropic consideration of adsorption. The polymer–solvent interaction parameter–inverse temperature dependence was found to be linear, as expected.     

STATISTICAL MECHANICAL MODEL THEORY OF THE STABILITY OF O/W AND W/O MICROEMULSIONS

A theoretical model to clarify the molecular origin of the mechanical and thermal stabilities of O/W or W/O microemulsion is proposed in which the low concentration of surfactants (emulsifiers) is limited. We assume only a short range interaction between surfactants and a bending stiffness energy which expresses the deformation energy from a preferable monolayer membrane curvature. We have found an interrelation among the interfacial pressure, Δp, of the monolayer due to the adsorption of surfactants in the microemulsion interface, interfacial tensions of oil-water interface and of the microemulsion, and the bending stiffness energy. We conclude that the interfacial tension and the stable form of the microemulsions (O/W type or W/O type) are infuenced largely by the effect of the bending stiffness energy. The interrelationship between the therraodynamical and mechanical stabilities of microemulsions is clarified by the use of our assumption.     

Curvature modulates the self-assembly of amphiphilic molecules

In this work, we used lattice Monte Carlo simulations and theoretical model calculations to show how the self-assembly of adsorbed amphiphilic molecules is affected by the local curvature of solid surfaces. It is found that, beyond a critical curvature value, solid surface geometry governs the spatial ordering of aggregates and may induce the morphological transitions. The simulation results show how the curvature of solid surfaces modulates the distribution of aggregates: the anisotropy in local curvature along and perpendicular to the cylindrical surfaces tends to generate orientationally ordered cylindrical micelles. To account for the morphological transitions induced by the local curvature of solid surfaces, we constructed a theoretical model which includes the Helfrich bending energy, the deformation energy of aggregates induced by solid surfaces, and the adsorption energy. The model calculations indicate that on highly curved solid surfaces the bending energy for bilayer structure sharply increases with surface curvature, which in turn induces the morphological transition from bilayer to cylindrical structure. Our results suggest that the local curvature provides a means of controlling the spatial organization of amphiphilic molecules.     

Investigation of interfacial and structural properties of CTAB at the oil/water interface using dissipative particle dynamics simulations

We have used dissipative particle dynamics (DPD) to simulate the system of cetyltrimethylammonium bromide (CTAB) monolayer at the oil/water interface. The interfacial properties (interfacial density, interfacial thickness, and interfacial tension), structural properties (area compressibility modulus, end to end distance, and order parameter), and their dependence on the oil/water ratio and the surfactant concentration were investigated. Three different microstructures, spherical oil in water (o/w), interfacial phase, and water in oil (w/o), can be clearly observed with the oil/water ratio increasing. Both the snapshots and the density profiles of the simulation show that a well defined interface exists between the oil and water phases. The interface thickens with CTAB concentration and oil/water ratio. The area compressibility modulus decreases with an increase in the oil/water ratio. The CTAB molecules are more highly packed at the interface and more upright with both concentration and oil/water ratio. The root mean square end-to-end distance and order parameter have a very weak dependence on the oil/water ratio. But both of them show an increase with CTAB concentration, indicating that the surfactant molecules at the interface become more stretched and more ordered at high concentration. As CTAB concentration increases further, the order parameter decreases instead because the bending of the interface. At the same time, it is shown that CTAB has a high interfacial efficiency at the oil/water interface.     

Effect of pH on the adsorption kinetics of egg yolk at the triacylglycerol–water interface and viscoelastic properties of interfacial egg yolk films: a dynamic drop tensiometry study

Interfacial properties of normal egg yolk (EY), as well as stabilized, i.e. enzymatically modified with phospholipase A2, egg yolk (SEY) at the triacylglyceride (TAG) oil–water interface have been investigated with the use of the dynamic drop tensiometry (DDT) technique in the wide interval of pH values of aqueous EY solutions. We found that for both EY and SEY pH values of their aqueous solutions affect absolute values of interfacial tension at the TAG oil–water interface. In the presence of EY this effect was more pronounced, with minimum of interfacial tension values at pH nearly equal to the isoelectric point of EY proteins. For SEY solutions no clear trend was noticed, although a reduction of interfacial tension near pH 6 was also observed. Moreover, the pH-dependence of nearly steady values of interfacial tension in the presence of EY was substantially less pronounced than it has been reported previously. It was also found that there is a difference in the interfacial viscoelasticity of SEY and EY films formed at the TAG oil–water interface. Although the dependence of dilational modulus, ∣ε∣, versus surface pressure for SEY solutions goes through a maximum, absolute values of ∣ε∣ increase for EY solutions in a wide pH range. At the same time, no visible effect of pH on the viscoelasticity of EY and SEY interfacial films was noticed. It became clear from the dilational modulus versus surface pressure curves for both EY and SEY that adsorption of their surface-active components at the TAG oil–water interface occurs in a step-wise manner. We found also that the phase angle values for the adsorbed EY layers were lower that those observed in the presence of SEY, indicating an increasing viscous contribution to the dilational modulus in the SEY-containing system.     

Interfacial tension of evaporating emulsion droplets containing amphiphilic block copolymers: effects of solvent and polymer composition

Evaporating droplets of volatile organic solvent containing amphiphilic block copolymers may undergo hydrodynamic instabilities that lead to dispersal of copolymer micelles into the surrounding aqueous phase. As for related phenomena in reactive polymer blends and oil/water/surfactant systems, this process has been ascribed to a nearly vanishing or transiently negative interfacial tension between the water and solvent phases induced by adsorption of copolymer to the interface. In this report, we investigate the influence of the choice of organic solvent and polymer composition for a series of polystyrene-b-poly(ethylene oxide) (PS-PEO) diblock copolymers, by in situ micropipette tensiometry on evaporating emulsion drops. These measurements suggest that the sensitivity to the organic solvent chosen reflects both differences in the bare solvent/water interfacial tension as well as the propensity of the copolymer to aggregate within the organic phase. While instabilities coincident with an approach of the interfacial tension nearly to zero were observed only for copolymers with PEO content greater than 15 wt.%, beyond this point the interfacial behavior and critical concentration needed to trigger surface instability were found to depend only weakly on copolymer composition.     

Surface tension and tolman length of spherical particulate in contact with fluid

The structure, surface tension and Tolman length of particulate-fluid interfaces were studied theoretically. Within the framework of density functional theory, the nonlocal, modified fundamental measure theory and direct correlation function from the first-order mean spherical approximation were incorporated. The theory accurately predicted the structure of fluid and the particulate-vapor surface tensions. The predictions of surface tensions for particulate-liquid interface and particulate in supercritical fluid are also reasonable. Especially, Tolman lengths for particulate-fluid interfaces were investigated systematically. The correct prediction of surface tension from Tolman length indicates that our analysis is reliable. Furthermore, Tolman length as a function of spherical particulate diameter, particulate-fluid interaction energy, and the properties of the fluid is fully discussed.     

Effect of Molecular Weight on the Interfacial Dilational Viscoelasticity of Anionic Polyelectrolyte/Surfactant Systems

In this article, the effect of molecular weight on the interfacial tension and interfacial dilational viscoelasticity of polystyrene sulfonate/surfactant adsorption films at the water-octane interface have been studied by spinning drop method and oscillating barriers method respectively. The experimental results show that different interfacial behaviors can be observed in different type of polyelectrolyte/surfactant systems. PSS/cationic surfactant CTAB systems show the classical behavior of oppositely charged polyelectrolyte/surfactant systems and can be well explained by electrostatic interaction. Molecular weight of PSS plays a crucial role in the nature of adsorption film. The complex formed by CTAB and higher molecular weight PSS, which has larger dimension and stronger interaction, results in higher dilational modulus at lower surfactant bulk concentration. In the case of PSS/anionic surfactant SDS systems, the co-adsorption of PSS at interface through hydrophobic interaction with alkyl chain of SDS leads to the increase of interfacial tension and the decrease of dilational modulus at lower surfactant bulk concentration. For PSS/nonionic surfactant T × 100 systems, PSS may form a sublayer contiguous to the aqueous phase, which has little effect on interfacial tension but slightly decreases dilational modulus.     

Adsorption of colloidal particles to curved interfaces

As a simple model for a Pickering emulsion droplet, we consider the adsorption of spherical particles to a spherical liquid-liquid interface in order to investigate the curvature effect on the particle adsorption. By taking into account both the surface and the volume energies due to the presence of a particle, we show that the equilibrium contact angle is determined by the classical Young's equation although the adsorption energy depends on the curvature. We also calculate the partitioning of the colloidal particles among the two liquids and the interface. The distribution of colloidal particles is expressed in terms of the interfacial curvature as well as the relative wettability of the particle.     

First correction to surface tension for the curvature of an interface

Tolman parameter δ_T, which determines the first correction to surface tension for the interface curvature, is calculated in molecular-dynamic experiments performed for Lennard-Jones fluid within the temperature range from the critical to the triple point (and slightly below). It is shown that parameter δ_T is positive and slightly depends on temperature; its absolute magnitude is no larger than 0.1–0.2 molecular diameters and does not coincide with the distance between the equimolecular dividing surface and the surface of tension in a flat interfacial layer, as calculated through the first moment of the pressure tensor. The results of the moleculardynamic experiments are compared with the δ_T values calculated in terms of the extended version of the van der Waals theory of capillarity. It is established that taking into account terms of higher orders than the squared density gradient in the expansion of the free energy of an inhomogeneous system does not reverse the negative sign at δ_T and slightly affects its value.     

Solubilization and phase equilibria of water-in-oil microemulsions : II. Effects of alcohols, oils, and salinity on single-chain surfactant systems

The solubilization and phase equilibria of w/o microemulsions have been shown to be dependent on two phenomenological parameters, namely the spontaneous curvature and elasticity of the interfacial film, when interfacial tension is very low. The spontaneous curvature of an interface is basically determined by the geometric packing of surfactant and cosurfactant molecules at the interface, whereas the interfacial elasticity is related to the energy required to bend the interface. The droplet size and solubilization of microemulsions is mainly determined by the radius of spontaneous curvature, and is further influenced by interfacial elasticity and interdroplet interactions. A w/o microemulsion with a highly curved and relatively rigid interfacial film can exist in equilibrium with excess water at the solubilization limit due to the interfacial bending stress. Increasing the natural radius and fluidity of the interface can increase the droplet size and hence the solubilization in the microemulsion. On the other hand, a w/o microemulsion with a highly fluid interfacial film can exist in equilibrium with an excess oil phase containing a low density of microemulsion droplets due to attractive interdroplet interaction. Increasing the interfacial rigidity and decreasing the natural radius in this case can increase water solubilization in the microemulsion by retarding the phase separation process. Thus, a maximum water solubilization in a w/o microemulsion can be obtained by minimizing both the interfacial bending stress of rigid interfaces and the attractive interdroplet interaction of fluid interfaces at an optimal interfacial curvature and elasticity. The study of phase equilibria of microemulsions can serve as a simple method to evaluate the property of the interface and provide phenomenological guidance for the formulation of microemulsions with maximum solubilization capacity.     

Effect of binding of an oligomeric cationic fluorosurfactant on the dilational rheological properties of gelatin adsorbed at the air-water interface

The effect of binding of an oligomeric cationic fluorooxetane surfactant on the interfacial properties of adsorbed gelatin-fluorooxetane complexes has been studied using dynamic surface tension and dilational rheological measurements. Adsorption kinetics of gelatin-fluorooxetane complexes are reminiscent of a mixed (barrier/diffusion limited) process, while the dilational rheological properties of the interface exhibit a strong dependence on surfactant concentration. At low surfactant concentrations, dilational surface moduli as well as phase angles are relatively insensitive to the presence of the fluorooxetane. However, at the critical aggregation concentration of the polymer-surfactant system, there is a sharp increase in the complex modulus. Further increase in the fluorooxetane concentration does not significantly affect the complex modulus. The phase angle, however, does increase with increasing fluorooxetane concentration due to the transport of bound fluorooxetane from the subsurface to the solution-air interface. These results indicate that, at fluorooxetane concentrations exceeding the critical aggregation concentration, the polymer-surfactant complexes adsorb to form cross-linked multilayers at the solution-air interface.     

TODGA/HNO_3萃取La~(3+)的界面性质

利用滴体积法研究了La~(3+)/HNO_3/N,N,N',N'-四辛基-3-氧戊二酰胺(TODGA)/稀释剂体系的界面性质,考察了TODGA浓度、液滴形成时间、稀释剂种类、La~(3+)浓度、体系温度、离子强度和溶液酸度等因素对体系界面性质的影响.实验结果表明,体系达到界面饱和吸附时间约为120 s,可认为体系达到萃取平衡;TODGA浓度不同时,界面张力也不同,进而判定界面饱和吸附物种亦不相同;极性较小的稀释剂体系的界面张力降低较大,按照正辛烷环己烷苯甲苯次序降低;HNO_3对TODGA的质子化作用使其表面活性显著增强,故硝酸浓度增大导致界面张力降低;Na NO_3的存在降低了界面上游离萃取剂分子的浓度,致使界面张力增大.     

Kelvin方程的一种理论推导

从液滴平衡条件推导出严格意义的Kelvin方程, 验证了其在宏观尺度可以转化为经典形式. 利用Tolman方程, 在考虑表面张力与曲率半径关系的条件下, 给出在液体压缩性可忽略时, 饱和蒸气压、蒸气密度、蒸气摩尔体积和曲率半径等关系; 液体压缩性不可忽略时, 得出以等温压缩系数和Tolman长度表示的饱和蒸气压与液滴半径的关系.     

Polar fluid model of viscoelastic membranes and interfaces

The polar surface fluid model is used to derive the generalized dynamic shape equation and the interfacial rheological material functions for viscoelastic membranes and curved interfaces, taking viscous bending and torsion modes into full account. The materials modeling approach based on the polar surface fluid leads to the integration of bending and torsion dissipative modes with their elastic counterparts that appear in the dynamic shape equation and in the interfacial rheological functions. The covariant bending and torsion rates derived in this paper are shown to be related to the interfacial co-rotational derivative of the curvature tensor. The dynamic shape equation is used to analyze shape fluctuation in planar geometries, and to establish the role of bending dissipation in shape dynamics. The dynamic shape equation generalizes the static Helfrich shape equation by incorporating bending and torsion dissipation, and it generalizes the dynamic shape equation based on the Boussinesq-Scriven model by incorporating bending and torsion elasticity and dissipation.