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

Electrically Controlled Spreading of a Surfactant-Laden Droplet on a Viscoelastic Interface

Electrically induced dynamic spreading of a droplet on a soft surface is characterized by intricate interactions between the moving contact line and the substrate deformation, which are explained by a complex interaction between elastic recovery and viscous dissipation that take place simultaneously. Here, we highlight the significance of an additional modulation in the interfacial energy brought about by the distribution of surfactant molecules surrounding the droplet, which causes an increase in the droplet's spreading rate, rather than the expected decrease in it due to energy dissipation at the viscoelastic interface. We attribute this to repartitioning of the surface energy that results in the dynamic reduction in the solid-liquid interfacial tension, overcoming the substrate viscosity-induced attenuation in the spreading rate. Using a scaling theory on the ensuing change in the contact angle as the droplet spreads dynamically, we further offer quantitative insights into the observed spreading dynamics. These findings allow for the rationalization of the sensitive reliance of droplet spreading on the initial contact angle, a phenomenon that has not yet been understood, in addition to providing a scientific basis for dynamic regulation of droplet spreading on soft biomimetic interfaces.

Effect of molecular branching and surface wettability on solid-liquid surface tension and line-tension of liquid alkane surface nanodroplets

HYPOTHESIS

Surface nanodroplets have important technological applications. Previous experiments and simulations have shown that their contact angle deviates from Young's equation. A modified version of Young's equation considering the three-phase line tension (τ) has been widely used in literature, and a wide range of values for τ are reported. We have recently shown that molecular branching affects the liquid-vapour surface tension γlv of liquid alkanes. Therefore, the wetting behaviour of surface nanodroplets should be affected by molecular branching. This study conducted molecular dynamics (MD) simulations to gain insight into the wetting behaviour of linear and branched alkane nanodroplets on oleophilic and oleophobic surfaces. We aim to examine the Young equation's validity and branching's effect on fundamental properties, including solid-liquid surface tension γsl and line tension τ.

SIMULATIONS

The simulations were performed on a linear alkane, triacontane (C30H62), as well as four of its branched isomers: 2,6,13,17-tetrapropyloctadecane,2,6,9,10,13,17-hexaethyloctadecane, 2,5,7,8,11,12,15-heptaethylhexadecane and 2,3,6,7,10,11-hexapropyldodecane. Nanodroplets with a diameter of approximately 15 nm were released onto the surfaces, and their contact angles were measured. Additionally, using a novel approach, the solid-liquid surface tension (γsl), the validity of Young's equation and line tension for all alkane and surface combinations are determined.

FINDINGS

It was discovered that the calculated γsl, deviated from the theoretical γsl,Young predicted from Young's equation for all alkanes on oleophilic surfaces. However, this deviation was minimal for branched alkanes on the oleophobic surfaces but more significant for the linear alkane. The findings indicated that γsl < 0 for oleophilic surfaces and γsl > 0 for oleophobic surfaces. Moreover, it was observed that |γsl| was lower for branched molecules and decreased as branching increased. Line tension values were then determined through a novel method, showing τ was positive for oleophilic surfaces ranging from 1.30 × 10-10 to 6.27 × 10-11N. On an oleophobic surface, linear alkane shows a negative line tension of -1.15 × 10-10N and branched alkanes up to two orders of magnitude lower values ranging from -2.09 × 10-12 to 2.43 × 10-11N. Line tension values between -1.15 × 10-10 and + 1.1 × 10-10N are calculated for various linear alkane and surface combinations. These findings show the dependence of line tension on the contact angle and branching, demonstrating that for linear alkanes, τ is significant, whereas, for branched alkanes, line tension is smaller or negligible for large contact angles.

Molecular Dynamics Study on the Wettability of the Lithium Droplet and Tungsten Surface

In this paper, molecular dynamics (MD) simulation was used to study the wettability of lithium and tungsten. The surface energy barrier and evaporation control the static contact angle with increasing temperature. The effects of 4 different sizes of droplets and 10 different tungsten sections were evaluated. Moreover, it was found that the different arrangements of atoms on the solid surface will affect the wettability, but the size of the droplet has little effect. In addition, the situation of the droplets driven by six different external forces was evaluated. When the force increases, the two states of the droplet and stream will have different properties. Finally, we studied the phase behavior between lithium and tungsten. For example, lithium overflows from the tungsten plate. The tungsten phase is separated in the lithium plate. Lithium is faster than tungsten when it aggregates in the gas phase, and wettability will drive the effects of engulfing and spitting.

Line Tension and Drop Size Dependence of Contact Angle at the Nanoscale

Despite considerable research efforts, the influence of contact line tension during wetting at the nanoscale and its experimental determination remain challenging tasks. So far, molecular dynamics simulations and atomic force microscope measurements have contributed to the understanding of these phenomena. However, a direct measurement of the size dependence of the contact angle and the magnitude of the apparent line tension has not been realized so far. Here, we show that the contact angle is indeed dependent on the drop size for small drop diameters and determine the magnitude of the apparent line tension via liquid-metal based measurements of advancing and receding contact angle inside a scanning electron microscope. For this purpose, a robotic setup inside an electron microscope chamber and oxide-free Galinstan droplets-produced via an electromigration-based and focused ion beam irradiation-assisted process-are employed. Using the first-order correction of Young's equation, we find an apparent line tension value of 4.02 × 10-7 J/m for Galinstan© on stainless steel.

Wetting Behavior of a Surface with Dual-Scale Structures

Theoretical and numerical studies were conducted to investigate the transitional interpillar spacing for dual-scale structures, where wetting transition between the Wenzel and Cassie-Baxter states occurs in the primary and secondary pillars. A theoretical formula was derived for the transitional interpillar spacing based on the continuum picture of water. Molecular dynamics (MD) simulations were carried out by varying the interpillar spacing for the primary pillars for single- and dual-scale structures with various pillar heights. The results obtained from the theoretical formula agreed reasonably well with the results obtained from MD simulations, especially when the primary pillar height was relatively high. The transitional interpillar spacing increases as the pillar height and the number of secondary pillars increase. The effect of the secondary pillars on the transitional interpillar spacing was also evaluated using the difference in the grand potentials between the Wenzel and Cassie-Baxter states. These results show that the dual-scale structures increase the transitional interpillar spacing with an increase in the surface hydrophobicity.

Investigations into the Complete Spreading Dynamics of a Viscoelastic Drop on a Spherical Substrate

We study the spreading dynamics of a sphere-shaped elastic non-Newtonian liquid drop on a spherical substrate in the capillary-driven regime. We use the simplified Phan-Thien-Tanner model to represent the rheology of the elastic non-Newtonian drop. We consider the drop to be a crater on a flat substrate to calculate the viscous dissipation near the contact line. Following the approach compatible with the capillary-viscous force balance, we establish the evolution equation for describing the temporal evolution of the contact line during spreading. We show that the contact line velocity obtained from the theoretical calculation matches well with our experimental observations. Also, as confirmed by the present experimental observations, our analysis deems efficient to capture the phenomenon during the late stage of spreading for which the effect of line tension becomes dominant. An increment in the viscoelastic parameter of the fluid increases the viscous dissipation effect at the contact line. It is seen that the higher dissipation effect leads to an enhancement in the wetting time of the drop on the spherical substrate. Also, we have shown that the elastic nature of the fluid leads to an increment in the dynamic contact angle at any temporal instant as compared to its Newtonian counterpart. Finally, we unveil that the phenomenon of the increasing contact angle results in the time required for the complete wetting of drop, which becomes higher with increasing viscoelasticity of the fluid. This article will fill a gap still affecting the existing literature because of the unavailability of experimental investigations of the spreading of the elastic non-Newtonian drop on a spherical substrate.

A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.

Size dependent influence of contact line pinning on wetting of nano-textured/patterned silica surfaces

Wetting behavior on a heterogeneous surface undergoes contact angle hysteresis as the droplet stabilized at a metastable state with a contact angle significantly different from its equilibrium value due to contact line pinning. However, there is a lack of consensus on how to calculate the influence of pinning forces. In general, the pinning effect can be characterized as (i) microscopic behavior when a droplet is pinned and the contact angle increases/decreases as the droplet volume increases/decreases and (ii) macroscopic behavior as the pinning effects decrease and ultimately, disappear with the increase of the droplet size. The current work studied both behaviors using molecular dynamics (MD) simulation with more than 300 different size water droplets on silica surfaces with three different patterns across two different wetting conditions. Results showed that the contact angle increases linearly with increasing droplet volume through the microscopic behavior, while the droplet is pinned on top of a certain number of patterns. When we normalized the droplet size with the corresponding pattern size, we observed a "wetting similarity" that linear microscopic contact angle variations over different size heterogeneities continuously line up. This shows that the pinning force remains constant and the resulting pinning effects are scalable by the size ratio between the droplet and pattern, independent of the size-scale. The slope of these microscopic linear variations decreases with an increase in the droplet size as observed through the macroscopic behavior. We further found a universal behavior in the variation of the corresponding pinning forces, independent of the wetting condition. In macroscopic behavior, pinning effects become negligible and the contact angle reaches the equilibrium value of the corresponding surface when the diameter of the free-standing droplet is approximately equal to 24 times the size of the surface structure. We found that the pinning effect is scalable with the droplet volume, not the size of the droplet base.

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.

What Is the Value of Water Contact Angle on Silicon?

Silicon is a widely applied material and the wetting of silicon surface is an important phenomenon. However, contradictions in the literature appear considering the value of the water contact angle (WCA). The purpose of this study is to present a holistic experimental and theoretical approach to the WCA determination. To do this, we checked the chemical composition of the silicon (1,0,0) surface by using the X-ray photoelectron spectroscopy (XPS) method, and next this surface was purified using different cleaning methods. As it was proved that airborne hydrocarbons change a solid wetting properties the WCA values were measured in hydrocarbons atmosphere. Next, molecular dynamics (MD) simulations were performed to determine the mechanism of wetting in this atmosphere and to propose the force field parameters for silica wetting simulation. It is concluded that the best method of surface cleaning is the solvent-reinforced de Gennes method, and the WCA value of silicon covered by SiO₂ layer is equal to 20.7° (at room temperature). MD simulation results show that the mechanism of pure silicon wetting is similar to that reported for graphene, and the mechanism of silicon covered by SiO₂ layer wetting is similar to this observed recently for a MOF.

Resolving the Apparent Line Tension of Sessile Droplets and Understanding its Sign Change at a Critical Wetting Angle

Despite strenuous research efforts for more than one century, identifying the magnitude and sign of the apparent line tension for a liquid-solid-gas system remains an elusive goal. Herein we accurately determine the apparent line tension from the size-dependent contact angle of sessile nanodrops on surfaces with different wetting properties via atomic force microscopy measurements and molecular dynamics simulations. We show that the apparent line tension has a magnitude of 10^{-11}-10^{-10}  J/m, in good agreement with theoretical predictions. Furthermore, while it is positive and favors shorter contact lines for droplets on very lyophilic surfaces, the apparent line tension changes its sign and favors longer contact lines on surfaces with an apparent contact angle higher than a critical value. By analyzing the density and the potential energy of liquid molecules within the sessile droplet, we demonstrate that the sign of the apparent line tension is a thermodynamic property of the liquid-solid-gas system rather than the local effect of intermolecular interactions in the three-phase confluence region.

Wettability of graphene: from influencing factors and reversible conversions to potential applications

As a member of the carbon material family, graphene has long been the focus of research on account of its abundant excellent properties. Nevertheless, many previous research works have attached much importance to its mechanical capacity and electrical properties, and not to its surface wetting properties with respect to water. In this review, a series of methods are put forward for characterization of the water contact angle of graphene, such as experimental measurements, classic molecular dynamics simulations, and formula calculations. A series of factors that affect the wettability of graphene, including defects, controllable atmosphere, doping, and electric field, are also discussed in detail, and have rarely have been covered in other review articles before. Finally, with the developments of smart surfaces, a reversible wettability variation of graphene from hydrophobic to hydrophilic is important in the presence of external stimulation and is discussed in detail herein. It is anticipated that graphene could serve as a tunable wettability coating for further developments in electronic devices and brings a new perspective to the construction of smart material surfaces.

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.

Entropy Contribution to the Line Tension: Insights from Polymer Physics, Water String Theory, and the Three-Phase Tension

The notion of three-phase (line) tension remains one of the most disputable notions in surface science. A very broad range of its values has been reported. Experts even do not agree on the sign of line tension. The polymer-chain-like model of three-phase (triple) line enables rough estimation of entropic input into the value of line tension, estimated as Γen≅kBTdm≅10−11N, where dm is the diameter of the liquid molecule. The introduction of the polymer-chain-like model of the triple line is justified by the “water string” model of the liquid state, predicting strong orientation effects for liquid molecules located near hydrophobic moieties. The estimated value of the entropic input into the line tension is close to experimental findings, reported by various groups, and seems to be relevant for the understanding of elastic properties of biological membranes.

Water graphene contact surface investigated by pairwise potentials from force-matching PAW-PBE with dispersion correction

A pairwise additive atomistic potential was developed for modeling liquid water on graphene. The graphene-water interaction terms were fit to map the PAW-PBE-D3 potential energy surface using the adaptive force matching method. Through condensed phase force matching, the potential developed implicitly considers the many-body effects of water. With this potential, the graphene-water contact angle was determined to be 86° in good agreement with a recent experimental measurement of 85° ± 5° on fully suspended graphene. Furthermore, the PAW-PBE-D3 based model was used to study contact line hysteresis. It was found that the advancing and receding contact angles of water do agree on pristine graphene, however a long simulation time was required to reach the equilibrium contact angle. For water on suspended graphene, sharp peaks in the water density profile disappear when the flexibility of graphene was explicitly considered. The water droplet induces graphene to wrap around it leading to a slightly concave contact interface.

Size-Dependent Submerging of Nanoparticles in Polymer Melts: Effect of Line Tension

Adhesion of nanoparticles to polymer films plays a key role in various polymer technologies. Here we report experiments that reveal how silica nanoparticles adhere to a viscoelastic PMMA film above the glass transition temperature. The polymer was swollen with CO₂, closely matching the conditions of nanoparticle-nucleated polymer foaming. It is found that the degree by which the particles sink into the viscoelastic substrate is strongly size dependent and can even lead to complete engulfment for particles of diameter below 12 nm. These findings are explained quantitatively by a thermodynamic analysis, combining elasticity, capillary adhesion, and line tension. We argue that line tension, here proposed for the first time in elastic media, is responsible for the nanoparticle engulfment.

Finite-Size and Solvent Dependent Line Tension Effects for Nanoparticles at the Air-Liquid Surface

The line tension for a nanoparticle (NP) at the air-liquid surface can be determined by examining the variation in NP solution surface tension with bulk NP concentration. In this publication the variation in line tension with liquid solvent is examined for the homologous series of liquids from n-decane through to n-octadecane. Finite-size line tension effects are also studied by examining the variation in line tension with NP size for NPs at the air-octadecane surface. Both the line tension variation with solvent and NP size can be qualitatively explained using an interface displacement model for the line tension.

Development of non-bonded interaction parameters between graphene and water using particle swarm optimization

New Lennard-Jones parameters have been developed to describe the interactions between atomistic model of graphene, represented by REBO potential, and five commonly used all-atom water models, namely SPC, SPC/E, SPC/Fw, SPC/Fd, and TIP3P/Fs by employing particle swarm optimization (PSO) method. These new parameters were optimized to reproduce the macroscopic contact angle of water on a graphene sheet. The calculated line tension was in the order of 10^-11 J/m for the droplets of all water models. Our molecular dynamics simulations indicate the preferential orientation of water molecules near graphene-water interface with one OH bond pointing toward the graphene surface. Detailed analysis of simulation trajectories reveals the presence of water molecules with ≤∼1, ∼2, and ∼4 hydrogen bonds at the surface of air-water interface, graphene-water interface, and bulk region of the water droplet, respectively. Presence of water molecules with ≤∼1 and ∼2 hydrogen bonds suggest the existence of water clusters of different sizes at these interfaces. The trends observed in the libration, bending, and stretching bands of the vibrational spectra are closely associated with these structural features of water. The inhomogeneity in hydrogen bond network of water at the air-water and graphene-water interface is manifested by broadening of the peaks in the libration band for water present at these interfaces. The stretching band for the molecules in water droplet shows a blue shift as compared to the pure bulk water, which conjecture the presence of weaker hydrogen bond network in a droplet. © 2017 Wiley Periodicals, Inc.

Spreading law of non-Newtonian power-law liquids on a spherical substrate by an energy-balance approach

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θ∼t^{-α} with the spreading exponent α, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

Spreading law on a completely wettable spherical substrate: The energy balance approach

The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The nonequilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension effect. Then the energy balance approach is adopted to derive the evolution equation of the spreading droplet. The time evolution of the contact angle θ of a droplet obeys a power law θ∼t^{-α} with the exponent α, which is different from that derived from Tanner's law on a flat substrate. Furthermore, the line tension must be positive to promote complete wetting on a spherical substrate, while it must be negative on a flat substrate.

Thermostability analysis of line-tension-associated nucleation at a gas-liquid interface

The influence of line tension on the thermostability of a droplet nucleated from an oversaturated vapor at the interface of the vapor and another immiscible liquid is investigated. Along with the condition of mechanical equilibrium, the notion of extremization of the reversible work of formation is considered to obtain the critical parameters related to heterogeneous nucleation. From the energetic formulation, the critical reversible work of formation is found to be greater than that of homogeneous nucleation for high value of the positive line tension. On the other hand, for high value of the negative line tension, the critical reversible work of formation becomes negative. Therefore, these thermodynamic instabilities under certain substrate wettability situations necessitate a free-energetics-based stability of the nucleated droplet, because the system energy is not minimized under these conditions. This thermostability is analogous to the transition-based stability proposed by Widom [B. Widom, J. Phys. Chem. 99, 2803 (1995)]10.1021/j100009a041 in the case of partial wetting phenomena along with the positive line tension. The thermostability analysis limits the domain of the solution space of the present critical-value problem as the thermodynamic transformation in connection with homogeneous and workless nucleation is considered. Within the stability range of the geometry-based wetting parameters, three limiting modes of nucleation, i.e., total-dewetting-related homogeneous nucleation, and total-wetting-associated and total-submergence-associated workless nucleation scenarios, are identified. Either of the two related limiting wetting scenarios of workless nucleation, namely, total wetting and total submergence, is found to be favorable depending on the geometry-based wetting conditions. The line-tension-associated nucleation on a liquid surface can be differentiated from that on a rigid substrate, as in the former, the stability based on mechanical equilibrium and a typical case of workless nucleation with complete submergence are observed.

Modeling the Hydrophobicity of Nanoparticles and Their Interaction with Lipids and Proteins

We present a method of modeling nanoparticle (NP) hydrophobicity using coarse-grained molecular dynamics (CG MD) simulations, and apply this to the interaction of lipids with nanoparticles. To model at a coarse-grained level the wettability or hydrophobicity of a given material, we choose the MARTINI coarse-grained force field, and determine through simulation the contact angles of MARTINI water droplets residing on flat regular surfaces composed of various MARTINI bead types (C1, C2, etc.). Each surface is composed of a single bead type in each of three crystallographic symmetries (FCC, BCC, and HCP). While this method lumps together several atoms (for example, one cerium and two oxygens of CeO₂) into a single CG bead, we can still capture the overall hydrophobicity of the actual material by choosing the MARTINI bead type that gives the best fit of the contact angle to that of the actual material, as determined by either experimental or all-atom simulations. For different MARTINI bead types, the macroscopic contact angle is obtained by extrapolating the microscopic contact angles of droplets of eight different sizes (containing N_w = 3224-22978 water molecules) to infinite droplet size. For each droplet, the contact angle was computed from a best fit of a circular curve to the droplet interface extrapolated to the first layer of the surface. We then examine how small nanoparticles of differing wettability interact with MARTINI dipalmitoylphosphotidylcholine (DPPC) lipids and SP-C peptides (a component of lung surfactant). The DPPC shows a transition from tails coating the nanoparticle to a hemimicelle coating the water-wet NP, as the contact angle of a water droplet on the surface is lowered below ∼60°. The results are relevant to developing a taxonomy describing the potential nanotoxicity of nanoparticle interactions with components in the lung.

Size-dependent contact angle and the wetting and drying transition of a droplet adsorbed onto a spherical substrate: Line-tension effect

The size-dependent contact angle and the drying and wetting morphological transition are studied with respect to the volume change for a spherical cap-shaped droplet placed on a spherical substrate. The line-tension effect is included using the rigorous formula for the Helmholtz free energy in the droplet capillary model. A morphological drying transition from a cap-shaped to a spherical droplet occurs when the substrate is hydrophobic and the droplet volume is small, similar to the transition predicted on a flat substrate. In addition, a morphological wetting transition from a cap-shaped to a wrapped spherical droplet occurs for a hydrophilic substrate and a large droplet volume. The contact angle depends on the droplet size: it decreases as the droplet volume increases when the line tension is positive, whereas it increases when the line tension is negative. The spherical droplets and wrapped droplets are stable when the line tension is positive and large.

Free-Energy Barrier of Filling a Spherical Cavity in the Presence of Line Tension: Implication to the Energy Barrier between the Cassie and Wenzel States on a Superhydrophobic Surface with Spherical Cavities

The free-energy barrier of filling a spherical cavity having an inner wall of various wettabilities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of 180° to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall, resulting in an equilibrium contact angle of 0° to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel states of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat, and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.

Line tension and morphology of a sessile droplet on a spherical substrate

The effects of line tension on the morphology of a sessile droplet placed on top of a convex spherical substrate are studied. The morphology of the droplet is determined from the global minimum of the Helmholtz free energy. The contact angle between the droplet and the spherical substrate is expressed by the generalized Young's formula. When the line tension is positive and large, the contact angle jumps discontinuously to 180^{∘}, the circular contact line shrinks towards the top of the substrate, and the droplet detaches from the substrate, forming a spherical droplet if the substrate is hydrophobic (i.e., the Young's contact angle is large). This finding is consistent with that predicted by Widom [J. Phys. Chem. 99, 2803 (1995)JPCHAX0022-365410.1021/j100009a041]; the line tension induces a drying transition on a flat substrate. On the other hand, the contact angle jumps to 0^{∘}, the circular contact line shrinks towards the bottom of the substrate, and the droplet spreads over the substrate to form a wrapped spherical droplet if the substrate is hydrophilic (i.e., the Young's contact angle is small). Therefore, not only the drying transition of a cap-shaped to a detached spherical droplet but also the wetting transition of a cap-shaped to a wrapped spherical droplet could occur on a spherical substrate as the surface area of the substrate is finite. When the line tension is negative and its magnitude increases, the contact line asymptotically approaches the equator from either above or below. The droplet with a contact line that coincides with the equator is an isolated, singular solution of the first variational problem. In this instance, the contact line is pinned and cannot move as far as the line tension is smaller than the critical magnitude, where the wetting transition occurs.

Confinement Correction to Mercury Intrusion Capillary Pressure of Shale Nanopores

We optimized potential parameters in a molecular dynamics model to reproduce the experimental contact angle of a macroscopic mercury droplet on graphite. With the tuned potential, we studied the effects of pore size, geometry, and temperature on the wetting of mercury droplets confined in organic-rich shale nanopores. The contact angle of mercury in a circular pore increases exponentially as pore size decreases. In conjunction with the curvature-dependent surface tension of liquid droplets predicted from a theoretical model, we proposed a technique to correct the common interpretation procedure of mercury intrusion capillary pressure (MICP) measurement for nanoporous material such as shale. Considering the variation of contact angle and surface tension with pore size improves the agreement between MICP and adsorption-derived pore size distribution, especially for pores having a radius smaller than 5 nm. The relative error produced in ignoring these effects could be as high as 44%--samples that contain smaller pores deviate more. We also explored the impacts of pore size and temperature on the surface tension and contact angle of water/vapor and oil/gas systems, by which the capillary pressure of water/oil/gas in shale can be obtained from MICP. This information is fundamental to understanding multiphase flow behavior in shale systems.

Effect of a triple contact line on the thermokinetics of dropwise condensation on an immiscible liquid surface

An extended thermokinetic model is developed for liquid-substrate-induced condensation by considering the collective influence of the line tension and the two mechanisms of molecular transport.

Thermokinetics of heterogeneous droplet nucleation on conically textured substrates

Within the framework of the classical theory of heterogeneous nucleation, a thermokinetic model is developed for line-tension-associated droplet nucleation on conical textures considering growth or shrinkage of the formed cluster due to both interfacial and peripheral monomer exchange and by considering different geometric configurations. Along with the principle of free energy extremization, Katz kinetic approach has been employed to study the effect of substrate conicity and wettability on the thermokinetics of heterogeneous water droplet nucleation. Not only the peripheral tension is found to have a considerable effect on the free energy barrier but also the substrate hydrophobicity and hydrophilicity are observed to switch over their roles between conical crest and trough for different growth rates of the droplet. Besides, the rate of nucleation increases and further promotes nucleation for negative peripheral tension as it diminishes the free energy barrier appreciably. Moreover, nucleation inhibition can be achievable for positive peripheral tension due to the enhancement of the free energy barrier. Analyzing all possible geometric configurations, the hydrophilic narrower conical cavity is found to be the most preferred nucleation site. These findings suggest a physical insight into the context of surface engineering for the promotion or the suppression of nucleation on real or engineered substrates.

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.

Progress on the Surface Nanobubble Story: What is in the bubble? Why does it exist?

Interfaces between aqueous solutions and hydrophobic solid surfaces are important in various areas of science and technology. Many researchers have found that forces between hydrophobic surfaces in aqueous solution are significantly different from the classical DLVO theory. Long-range attractive forces (non-DLVO forces) are thought to be affected by nanoscopic gaseous domains at the interfaces. This is a review of the latest research on nanobubbles at hydrophobic surfaces from experimental and simulation studies. The review focusses on non-intrusive optical view of surface nanobubbles and gas enrichment on solid surfaces by imaging and force mapping. By use of these recent experimental data in conjunction with molecular simulation work, all major theories on surface nanobubble formation and stability are critically reviewed. Even though the current body of research cannot comprehensively explain all properties of surface nanobubbles observed, the fundamental understanding has been significantly improved. Line tension has been shown to be incapable of explaining the contact angle of nanobubbles. Dense gas layer theory provides a new explanation on both large contact angle and long-time stability. The high density of gas in these domains may significantly affect the gas-water interface which is in line with some observation made on bulk nanobubbles. Along this line of inquiry, experimental and simulation effort should be focussed on measuring the density within surface nanobubbles and the properties of the gas water interface which may be the key to explaining the stability of these nanobubbles.

Effect of particle geometry on triple line motion of nano-fluid drops and deposit nano-structuring

We illustrate the importance of particle geometry on droplet contact line pinning, 'coffee-stain' formation and nano-structuring within the resulting rings. We present the fundamentals of pure liquid droplet evaporation and then discuss the effect of particles on the evaporation process. The resulting coffee-stain patterns and particle structuring within them are presented and discussed. In the second part, we turn our attention to the effect of particle geometry on the evaporation process. A wide range of particle shapes, categorised according to aspect ratio, from the simple shape of a sphere to the highly irregular shapes of platelets and tubes is discussed. Particle geometry effect on evaporation behaviour was quantified in terms of change in contact angle and contact radius for the stick-slip cases. Consequently the hysteretic energy barrier pinning the droplets was estimated, showing an increasing trend with particle aspect ratio. The three-phase contact line (TL) motion kinetics are complemented with analysis of the nano-structuring behaviour of each shape, leading to the identification of the two main parameters affecting nanoparticle self-assembly behaviour at the wedge. Flow velocity and wedge constraints were found to have antagonist effects on particle deposition, although these varied with particle shape. This description should help in understanding the drying behaviour of more complex fluids. Furthermore, knowing the fundamentals of this simple and inexpensive surface patterning technique should permit its tailoring to the needs of many potential applications.

Line-tension-induced scenario of heterogeneous nucleation on a spherical substrate and in a spherical cavity

Line-tension-induced scenario of heterogeneous nucleation is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the free energy of a critical nucleus can be separated from the usual volume term. By comparing the free energy of a lens-shaped critical nucleus of a finite contact angle with that of a spherical nucleus, we find that a spherical nucleus may have a lower free energy than a lens-shaped nucleus when the line tension is positive and large, which is similar to the drying transition predicted by Widom [B. Widom, J. Phys. Chem. 99, 2803 (1995)]. Then, the homogeneous nucleation rather than the heterogeneous nucleation will be favorable. Similarly, the free energy of a lens-shaped nucleus becomes negative when the line tension is negative and large. Then, the barrier-less nucleation with no thermal activation called athermal nucleation will be realized.

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.

Measurement of line tension on droplets in the submicrometer range

Wetting is a universal phenomenon in nature and of interest in fundamental research as well as in engineering sciences. Usually, wetting of solid substrates by liquid drops is described by Young's equation, which relates the contact angle between the liquid and the substrate to the three interfacial tensions. This concept has been widely used and confirmed for macroscopic droplets. On the contrary, it is still matter of debate to what extent this concept is able to explain relations on the micrometer scale and below. The so-called extended Young's equation, which takes account of the specific arrangement of the molecules in the three-phase contact line by implementing a term called "line tension", is frequently used to characterize deviations from the "ideal" Young's case. In this work we tried to look into the dependence of measured contact angles of droplets on their size for a close to ideal system. We measured contact angles of ionic liquid droplets with radii between some tens and some hundreds of nanometers by atomic force microscopy on an ideally flat silicon wafer. We found that the contact angles decreased with decreasing droplet size: smaller droplets showed stronger wetting. This dependence of the contact angle on the droplet radius could not be described with the concept of line tension or the modified Young's equation. We propose simple arguments for a possible alternative concept.

Dynamics of nanoscale droplets on moving surfaces

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.

Stability of thin wetting films on chemically nanostructured surfaces

The morphology and stability of thin volatile wetting films on model chemically patterned surfaces composed of periodic arrays of alternating completely and partially wettable nanostripes are investigated. The equilibrium film morphology is recorded as a function of undersaturation using noncontact atomic force microscopy. Films spanning the entire pattern are found to be stable only for thicknesses in excess of a critical value, h(c), whereas thinner films spontaneously dewet the partially wettable regions of the substrate. The critical thickness h(c) increases linearly with the width of the partially wettable stripes in good agreement with an interface displacement model derived from microscopic density functional theory. These results provide detailed insights into the dewetting of thin films driven by competing intermolecular forces.

Elastic modulus of a polymer nanodroplet: theory and experiment

We redevelop a theoretical model that, in conjunction with atomic force microscopy (AFM), can be used as a noninvasive method for determination of the elastic modulus of a polymer nanodroplet residing on a flat, rigid substrate. The model is a continuum theory that combines surface and elasticity theories for prediction of the droplet's elastic modulus, given experimental measurement of its adsorbed height. Utilization of AFM-measured heights for relevant droplets reported in the literature and from our own experiments illustrated the following: the significance of both surface and elasticity effects in determining a polymer droplet's spreading behavior; the extent of a continuum theory's validity as one approaches the nanoscale; and a droplet size effect on the elastic modulus.

Wetting transparency of graphene

We report that graphene coatings do not significantly disrupt the intrinsic wetting behaviour of surfaces for which surface-water interactions are dominated by van der Waals forces. Our contact angle measurements indicate that a graphene monolayer is wetting-transparent to copper, gold or silicon, but not glass, for which the wettability is dominated by short-range chemical bonding. With increasing number of graphene layers, the contact angle of water on copper gradually transitions towards the bulk graphite value, which is reached for ~6 graphene layers. Molecular dynamics simulations and theoretical predictions confirm our measurements and indicate that graphene's wetting transparency is related to its extreme thinness. We also show a 30-40% increase in condensation heat transfer on copper, as a result of the ability of the graphene coating to suppress copper oxidation without disrupting the intrinsic wettability of the surface. Such an ability to independently tune the properties of surfaces without disrupting their wetting response could have important implications in the design of conducting, conformal and impermeable surface coatings.