Theory of nucleated wetting

Line tension of sessile droplets: Thermodynamic considerations

We deduce a thermodynamically consistent diffuse interface model to study the line tension phenomenon of sessile droplets. By extending the standard Cahn-Hilliard model via modifying the free energy functional due to the spatial reflection asymmetry at the substrate, we provide an alternative interpretation for the wall energy. In particular, we find the connection of the line tension effect with the droplet-matrix-substrate triple interactions. This finding reveals that the apparent contact angle deviating from Young's law is contributed by the wall energy reduction as well as the line energy minimization. Besides, the intrinsic negative line tension resulting from the curvature effect is observed in our simulations and shows good accordance with recent experiments [Tan et al. Phys. Rev. Lett. 130, 064003 (2023)0031-900710.1103/PhysRevLett.130.064003]. Moreover, our model sheds light upon the understanding of the wetting edge formation which results from the vying effect of wall energy and line tension.

Nonclassical Surface Nucleation of 6CB at the Air-Liquid Interface of a 6CB Oil-in-Water Nanoemulsion

The surface tension of a freshly extruded pendant drop of a nanoemulsion, 4-cyano-4'-hexylbiphenyl or 6CB (a liquid crystal) in water, exhibits an unusual surface nucleation phenomenon. Initially the surface tension is that of pure water; however, after a surface nucleation time, the surface tension decreases suddenly in magnitude. This nucleation time, of hundreds to thousands of seconds, depends strongly upon (i) the 6CB concentration in water, (ii) the 6CB nanodroplet size, and (iii) the temperature. Similar behavior is observed in both the isotropic and nematic phases of 6CB; thus, this surface nucleation phenomenon is unrelated to this system's liquid crystalline properties. The observed surface nucleation behavior can be explained via considerations of the nanoemulsion's bulk entropy together with the number of 6CB nanodroplets in the vicinity of the surface.

Thinning and thickening transitions of foam film induced by 2D liquid-solid phase transitions in surfactant-alkane mixed adsorbed films

Mixed adsorbed film of cationic surfactant and linear alkane at the air-water interface shows two-dimensional phase transition from surface liquid to surface frozen states upon cooling. This surface phase transition is accompanying with the compression of electrical double layer due to the enhancement of counterion adsorption onto the adsorbed surfactant cation and therefore induces the thinning of the foam film at fixed disjoining pressures. However, by increasing the disjoining pressure, surfactant ions desorb from the surface to reduce the electric repulsion between the adsorbed films on the both sides of the foam film. As a result, the foam film stabilized by the surfactant-alkane mixed adsorbed films showed unique thickening transition on the disjoining pressure isotherm due to the back reaction to the surface liquid films. In this review, we will summarize all these features based on the previously published papers and newly obtained results.

Unique Interfacial Phenomena on Macroscopic and Colloidal Scales Induced by Two-Dimensional Phase Transitions

This feature article addresses a variety of unique macroscopic-scale and colloidal-scale interfacial phenomena, such as wetting transitions of oil droplets into molecularly thin films, spontaneous merging and splitting of oil droplets at air-water interfaces, solid monolayer and bilayer formation in mixed cationic surfactant/alkane adsorbed films, switching of foam-film thickness, and oil-in-water emulsion stability. All of these phenomena can be observed using commercial cationic surfactants, liquid alkanes, and water.

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.

Liquid droplet coalescence and fragmentation at the aqueous-air surface

For hexadecane oil droplets at an aqueous-air surface, the surface film in coexistence with the droplets exhibits two-dimensional gaseous (G), liquid (L), or solid (S) behavior depending upon the temperature and concentration of the cationic surfactant dodecyltrimethylammonium bromide. In the G (L) phase, oil droplets are observed to coalesce (fragment) as a function of time. In the coalescence region, droplets coalesce on all length scales, and the final state is a single oil droplet at the aqueous-air surface. The fragmentation regime is complex. Large oil droplets spread as oil films; hole nucleation breaks up this film into much smaller fluctuating and fragmenting or metastable droplets. Metastable droplets are small contact angle spherical caps and do not fluctuate in time; however, they are unstable over long time periods and eventually sink into the bulk water phase. Buoyancy forces provide a counterbalancing force where the net result is that small oil droplets (radius r < 80 μm) are mostly submerged in the bulk aqueous medium with only a small fraction protruding above the liquid surface. In the G phase, a mechanical stability theory for droplets at liquid surfaces indicates that droplet coalesce is primarily driven by surface tension effects. This theory, which only considers spherical cap shaped surface droplets, qualitatively suggests that in the L phase the sinking of metastable surface droplets into the bulk aqueous medium is driven by a negative line tension and a very small spreading coefficient.

Influence of contact-line curvature on the evaporation of nanodroplets from solid substrates

The effect of the three-phase contact-line curvature on the evaporation mechanism of nanoscopic droplets from smooth and chemically homogenous substrates is studied by molecular dynamics simulations. Spherical droplets, whose three-phase contact line is curved, and cylindrical droplets, whose contact radius is infinite, are compared. It is found that the evaporation of cylindrical droplets takes place at constant contact angle, while spherical droplets evaporate by simultaneous reduction of their contact area and their contact angle. This is independent of the substrate-liquid interaction strength. The dependence of the evaporation mechanism on the contact-line curvature can be rationalized with the help of the concept of a contact-line tension, and the evaporation simulations of the spherical droplets are used to extract the line tension on each surface. The corresponding values for the Lennard-Jones systems studied here are of the order of 10(-11)N, which is in a good agreement with previous theoretical and experimental estimates. With this order of magnitude, the line tension is expected to have an effect on the contact angle of spherical droplets only, when their diameter is less than about 100 nm. The observed difference in evaporation mechanism is interpreted as a manifestation of the line tension whose existence has been controversial.

Line tension of alkane lenses on aqueous surfactant solutions at phase transitions of coexisting interfaces

Alkane droplets on aqueous solutions of surfactants exhibit a first-order wetting transition as the concentration of surfactant is increased. The low-concentration or "partial wetting" state corresponds to an oil lens in equilibrium with a two-dimensional dilute gas of oil and surfactant molecules. The high-concentration or "pseudo-partial wetting" state consists of an oil lens in equilibrium with a mixed monolayer of surfactant and oil. Depending on the combination of surfactant and oil, these mixed monolayers undergo a thermal phase transition upon cooling, either to a frozen mixed monolayer or to an unusual bilayer structure in which the upper leaflet is a solid layer of pure alkane with hexagonal packing and upright chains while the lower leaflet remains a disordered liquid-like mixed monolayer. Additionally, certain long-chain alkanes exhibit a surface freezing transition at the air-oil interface where the top monolayer of oil freezes above its melting point. In this review, we summarize our previous studies and discuss how these wetting and surface freezing transitions influence the line tension of oil lenses from both an experimental and theoretical perspective.

Influence of line tension on spherical colloidal particles at liquid-vapor interfaces

Atomic force microscopy (AFM) imaging of isolated submicron dodecyltrichlorosilane coated silica spheres, immobilized at the liquid polystyrene- (PS-) air interface at the PS glass transition temperature, T(g), allows for determination of the contact angle θ versus particle radius R. At T(g), all θ versus R measurements are well described by the modified Young's equation for a line tension τ = 0.93 nN. The AFM measurements are also consistent with a minimum contact angle θ(min) and minimum radius R(min), below which single isolated silica spheres cannot exist at the PS-air interface.

Impact of negative line tension on the shape of nanometer-size sessile droplets

The sign and value of the line tension has been measured from the size dependence of the contact angle of nanometer-size sessile fullerene (C60) droplets on the planar SiO2 interface, measured with atomic force microscopy (AFM). Analysis according to the modified Young's equation indicates a negative line tension, with a magnitude between -10{-11} and -10{-10}  N/m, in good agreement with theoretical predictions. The experiments also indicate that droplets with contact area radii below 10 nm are in fact two-dimensional round terraces.

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid-fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. In addition we study a system containing a planar liquid-gas interface in contact with a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. Curvatures of interfaces are taken into account. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition, however, the line tension does depend on the choice of the Gibbs dividing interfaces. We also provide form invariant equations for the equilibrium contact angles which properly transform under notional shifts of dividing interfaces which change the description of the system but leave the density configurations unchanged. It is shown that in order to accomplish this form invariance, additional stiffness coefficients attributed to the contact line must be introduced. The choice of the dividing interfaces influences the actual values of the stiffness coefficients. We show how these coefficients transform as a function of the relative displacements of the dividing interfaces. Our formulation provides a clearly defined scheme to determine line properties from measured dependences of the contact angles on lens or drop volumes. This scheme implies relations different from the modified Neumann or Young equations, which currently are the basis for extracting line tensions from experimental data. These relations show that the experiments do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness coefficients of the line. In contrast to previous approaches our scheme works consistently for any choice of the dividing interfaces. It further allows us to compare results obtained by different experimental or theoretical methods, based on different conventions of choosing the dividing interfaces.

Line tension approaching a first-order wetting transition: experimental results from contact angle measurements

The line tension values of n-octane and 1-octene on a hexadecyltrichlorosilane coated silicon wafer, are determined by contact angle measurements at temperatures near a first-order wetting transition T(w). It is shown experimentally that the line tension changes sign as the temperature increases toward T(w) in agreement with a number of theoretical predictions. A simple phenomenological model possessing a repulsive barrier at l(0)=5.1+/-0.2 nm and a scale factor of B=78+/-6 provides a quantitative description of the experiments.