Macroscopic Contact Angle Research Articles

The importance of chemical potential in the determination of water slip in nanochannels.

We investigate the slip properties of water confined in graphite-like nanochannels by non-equilibrium molecular dynamics simulations, with the aim of identifying and analyze separately the influence of different physical quantities on the slip length. In a system under confinement but connected to a reservoir of fluid, the chemical potential is the natural control parameter: we show that two nanochannels characterized by the same macroscopic contact angle--but a different microscopic surface potential--do not exhibit the same slip length unless the chemical potential of water in the two channels is matched. Some methodological issues related to the preparation of samples for the comparative analysis in confined geometries are also discussed.

Effect of silica nanoparticles in mixed matrix membranes for pervaporation dehydration of acetic acid aqueous solution: plant-inspired dewatering systems

Clean technology in dehydration of acetic acid using pervaporative separations inspired by plant dewatering systems is studied in this work. The novel polyphenylsulfone-based membranes, modified with silica nanoparticles, were used to dehydrate a binary mixture of acetic acid and water. The Stöber process was applied for the synthesis of monodispersed silica colloids by hydrolysis of alkyl silicates and condensation of silicic acid in alcoholic solution. The surface free energy of the synthesized silica particles was altered through a silanization treatment with hexamethyldisilazane to convert the surface hydroxyl groups to trimethylsilyl[–Si(CH3)3] groups. The synthesized particles and the modified polyphenylsulfone based membranes were characterized using dynamic light scattering, scanning electron microscopy, atomic force microscopy, Fourier-transform infrared and macroscopic contact angle measurements. Pervaporation was used for the dehydration of 70 wt% acetic acid at 70 °C using nine different membrane variations. Inspired by the natural dewatering in plants containing silica, the performance of the synthetic silica nanoparticles filled-membranes was investigated. Similar to plants, the incorporation of silica nanoparticles in these membranes significantly affected the dewatering process. It was found that at higher concentrations of silica, an improvement of membrane properties was observed, particularly in terms of selectivity. Besides that, the hydrophilicity and surface roughness increases when sufficient amounts of silanols groups were present on the membrane surface. It was concluded that more hydrophilic silica should be first produced and incorporated into the membranes for efficient removal of water from acetic acid. This can be achieved by controlling the composition ratio of ammonium hydroxide, water and ethanol for the nanoparticle fabrication. The effect of different nanoparticle types on membrane morphology and pervaporation performance is also discussed in detail in this work.

Wettability of graphitic-carbon and silicon surfaces: MD modeling and theoretical analysis.

The wettability of graphitic carbon and silicon surfaces was numerically and theoretically investigated. A multi-response method has been developed for the analysis of conventional molecular dynamics (MD) simulations of droplets wettability. The contact angle and indicators of the quality of the computations are tracked as a function of the data sets analyzed over time. This method of analysis allows accurate calculations of the contact angle obtained from the MD simulations. Analytical models were also developed for the calculation of the work of adhesion using the mean-field theory, accounting for the interfacial entropy changes. A calibration method is proposed to provide better predictions of the respective contact angles under different solid-liquid interaction potentials. Estimations of the binding energy between a water monomer and graphite match those previously reported. In addition, a breakdown in the relationship between the binding energy and the contact angle was observed. The macroscopic contact angles obtained from the MD simulations were found to match those predicted by the mean-field model for graphite under different wettability conditions, as well as the contact angles of Si(100) and Si(111) surfaces. Finally, an assessment of the effect of the Lennard-Jones cutoff radius was conducted to provide guidelines for future comparisons between numerical simulations and analytical models of wettability.

Electrically modulated dynamic spreading of drops on soft surfaces

The intricate interaction between the deformability of a substrate and the dynamic spreading of a liquid drop on the same, under the application of an electrical voltage, has remained far from being well understood. Here, we demonstrate that electrospreading dynamics on soft substrates is dictated by the combined interplay of electrocapillarity, the wetting line friction and the viscoelastic energy dissipation at the contact line. Our results reveal that during such electro-elastocapillarity mediated spreading of a sessile drop, the contact radius evolution exhibits a universal power law in a substrate elasticity based non-dimensional time, with an electric potential dependent spreading exponent. Simultaneously, the macroscopic dynamic contact angle variation follows a general power law in the contact line velocity, normalized by elasticity dependent characteristic velocity scale. Our results are likely to provide the foundation for the development of a plethora of new applications involving droplet manipulations by exploiting the interplay between electrically triggered spreading and substrate-compliance over interfacial scales.

Wetting in [formula omitted] dimensions with two-scale roughness

We show that a two-scale model in 1+1 dimensions enhances superhydrophobicity. The two scales may differ by a factor of order two or three, or by a large factor in a scaling limit. In both cases, we compute explicitly the macroscopic contact angles as function of the flat material contact angle and aspect ratios. In addition to the Cassie–Baxter states with air cushion below the droplet and to the Wenzel states, completely wet, there appear several mixed states with air trapped in corners.

Quantifying Density Fluctuations in Water at a Hydrophobic Surface: Evidence for Critical Drying.

Employing smart MonteCarlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction, we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility χ(z), increase rapidly for distances z within one or two molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle θ, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: cos(θ)→-1. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.

Molecular Dynamics Study for Channel Size Dependence of Shear Stress Between Droplet and Wall.

In this study, the channel size dependence of the shear stress between water droplets and solid walls in nm-order channel was analyzed. We considered a several different-sized and highly hydrophobic channel whose macroscopic contact angle was about 150 degrees. We have evaluated the shear stress and the normal pressure by molecular dynamics simulation. Analyzing shear stress and normal pressure based on the macroscopic model, we have discussed the difference between the macroscopic model based on hydrodynamics and the microscopic model. As a result, in the high hydrophobic case, it became clear that the shear stress depends on the channel size due to the large Laplace pressure. Furthermore, in the case that the channel size was less than 50 A, the normal pressure by the molecular simulation didn't agree with the expected value from the Young-Laplace equation. From this study it was clear that molecular simulation is needed when the channel size is less than 40 A.

Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions.

A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θc), obtained from the generalized Young's equation and the stability analysis, is θ∞ < θc < θ' for positive line tension and is θM < θc < θ∞ for negative line tension. θ∞ is the macroscopic contact angle, θ' is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θM is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ∞ and higher values of θc for positive line tension. The combined effect due to the presence of the triple line and the interfacial areas (f(L) + f(S)) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θc(0 < θc < θ∞) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.

Macroscopic Theory for Capillary-Pressure Hysteresis

In this article, we present a theory of macroscopic contact angle hysteresis by considering the minimization of the Helmholtz free energy of a solid-liquid-gas system over a convex set, subject to a constant volume constraint. The liquid and solid surfaces in contact are assumed to adhere weakly to each other, causing the interfacial energy to be set-valued. A simple calculus of variations argument for the minimization of the Helmholtz energy leads to the Young-Laplace equation for the drop surface in contact with the gas and a variational inequality that yields contact angle hysteresis for advancing/receding flow. We also show that the Young-Laplace equation with a Dirichlet boundary condition together with the variational inequality yields a basic hysteresis operator that describes the relationship between capillary pressure and volume. We validate the theory using results from the experiment for a sessile macroscopic drop. Although the capillary effect is a complex phenomenon even for a droplet as various points along the contact line might be pinned, the capillary pressure and volume of the drop are scalar variables that encapsulate the global quasistatic energy information for the entire droplet. Studying the capillary pressure versus volume relationship greatly simplifies the understanding and modeling of the phenomenon just as scalar magnetic hysteresis graphs greatly aided the modeling of devices with magnetic materials.

Inscribing wettability gradients onto polymer substrates with different stiffness using corona discharge in point-to-plane geometry

We use direct current (DC) corona discharge to create wettability gradients on polymer surfaces. The inhomogeneous current density distribution due to a point-to-plane arrangement induces local changes of the wettability of polymer surfaces, resulting in macroscopic wettability gradients. We found that condensation of water vapor on the surface allows a more precise characterization of the wettability gradient than macroscopic contact angle measurements. Condensation experiments allow characterizing different zones with different wettability. The wettability pattern depends on the stiffness of the substrate. We conjecture that Coulomb interactions influence the spatial distribution of wettability. Indirect measurements of the electrostatic surface potential after exposure support this assumption.

B112 表面粗さがサブミクロンスケールの水の凝縮に与える影響(OS-8:マイクロ・ナノ熱工学(1))

We observed the condensation process of submicron-scale droplets on silicon (100) surface by using environmental scanning electron microscope. We found that the condensation growth of a submicron-sized droplet is classified into two modes. In the first mode, the contact angle is smaller than the macroscopic contact angle, which is the contact angle observed for millimeter-sized droplets, and increases linearly with time until reaching the macroscopic contact angle. In the second mode, which follows the first mode, the base diameter increases with time while the contact angle remains constant. The first mode is a growth mode peculiar to droplets with diameters less than 10 μm.

Ice and water droplets on graphite: a comparison of quantum and classical simulations.

Ice and water droplets on graphite have been studied by quantum path integral and classical molecular dynamics simulations. The point-charge q-TIP4P/F potential was used to model the interaction between flexible water molecules, while the water-graphite interaction was described by a Lennard-Jones potential previously used to reproduce the macroscopic contact angle of water droplets on graphite. Several energetic and structural properties of water droplets with sizes between 10(2) and 10(3) molecules were analyzed in a temperature interval of 50-350 K. The vibrational density of states of crystalline and amorphous ice drops was correlated to the one of ice Ih to assess the influence of the droplet interface and molecular disorder on the vibrational properties. The average distance of covalent OH bonds is found 0.01 Å larger in the quantum limit than in the classical one. The OO distances are elongated by 0.03 Å in the quantum simulations at 50 K. Bond distance fluctuations are large as a consequence of the zero-point vibrations. The analysis of the H-bond network shows that the liquid droplet is more structured in the classical limit than in the quantum case. The average kinetic and potential energy of the ice and water droplets on graphite has been compared with the values of ice Ih and liquid water as a function of temperature. The droplet kinetic energy shows a temperature dependence similar to the one of liquid water, without apparent discontinuity at temperatures where the droplet is solid. However, the droplet potential energy becomes significantly larger than the one of ice or water at the same temperature. In the quantum limit, the ice droplet is more expanded than in a classical description. Liquid droplets display identical density profiles and liquid-vapor interfaces in the quantum and classical limits. The value of the contact angle is not influenced by quantum effects. Contact angles of droplets decrease as the size of the water droplet increases which implies a positive sign of the line tension of the droplet.

Self-Propelled Motion of Oil Droplets on Au Electrode during Sn Electrodeposition

INTRODUCTIONIt was reported that macroscopic contact angles of an oil droplet put on an electrode surface decreased during electrodeposition of metals, such as Sn, Pb and Sb [1]. It was also reported that the difference in the contact angle between the front and rear sides of the droplet caused self-propelled lateral motion of the droplet [1]. This motion has attracted much interest from the viewpoint of the emergence of mechanical motion induced by chemical or electrochemical reactions.Little has been reported about the factors affecting the velocity of the motion. It has only been reported that the velocity increases with a negative shift in the electrode potential [1]. In this work, we studied the factors affecting the velocity and the mechanism of the motion.EXPERIMENTALThe self-propelled motion of a nitrobenzene droplet on an Au ring electrode was observed during Sn electrodeposition (Sn2+ + 2e- → Sn) in H2SO4 + 0.01 M SnSO4. The volume of the droplet was about 1.0 μL. Figure 1 shows schematic of the experimental setup. In order to study the dependence of the velocity on the density of the aqueous electrolyte, K2SO4was added to the electrolyte to increase the density.RESULTS and DISCUSSIONWe studied the dependence of the velocity on the electrode potential when the concentration of H2SO4was 0.5 M. As shown in Figure 2, the droplet did not move, i.e., the velocity was zero, in the potential region above ca. -0.44 V, though the Sn electrodeposition occurred. On the other hand, the droplet moved in the potential region below ca. -0.44 V where both the Sn electrodeposition and hydrogen evolution reaction (HER) occurred. The velocity increased with a negative shift in the electrode potential.In the potential region where the droplet moved, the Sn electrodeposition was limited by the mass-transport of Sn2+ions to the electrode surface, and hence the rate of electrodeposition was constant independently of the potential. We, therefore, think the velocity increase with a negative shift in the potential is probably attributed to the increase in the rate of the HER. Based on this idea, we suggest that the droplet motion is driven by the interaction between the Sn electrodeposition and the HER.We also studied the dependence of the velocity on the density of the aqueous electrolyte. As shown in Figure 3, the velocity observed at -0.66 V vs. SHE increased as the concentration of K2SO4increased. That is, the velocity increased as the density increased. The buoyancy of the droplet increased with the increasing density, which probably led to the increase in the velocity.This work is partially supported by the Research Institute for Science and Technology of Tokyo Denki University under Grants Q12E-02.REFERENCES [1] S. Nakanishi, T. Nagai, D. Ihara, Y. Nakato, Chemphyschem, 9 (2008) 2302-2304.

Visualization of asymmetric wetting ridges on soft solids with X-ray microscopy.

One of the most questionable issues in wetting is the force balance that includes the vertical component of liquid surface tension. On soft solids, the vertical component leads to a microscopic protrusion of the contact line, that is, a ‘wetting ridge’. The wetting principle determining the tip geometry of the ridge is at the heart of the issues over the past half century. Here we reveal a universal wetting principle from the ridge tips directly visualized with high spatio-temporal resolution of X-ray microscopy. We find that the cusp of the ridge is bent with an asymmetric tip, whose geometry is invariant during ridge growth or by surface softness. This singular asymmetry is deduced by linking the macroscopic and microscopic contact angles to Young and Neuman laws, respectively. Our finding shows that this dual-scale approach would be contributable to a general framework in elastowetting, and give hints to issues in cell-substrate interaction and elasto-capillary problems.

Thermally activated depinning motion of contact lines in pseudopartial wetting.

We investigate pressure-driven motion of liquid-liquid menisci in circular tubes, for systems in pseudopartial wetting conditions. The originality of this type of wetting lies in the coexistence of a macroscopic contact angle with a wetting liquid film covering the solid surface. Focusing on small capillary numbers, we report observations of an apparent contact angle hysteresis at first sight similar to the standard partial wetting case. However, this apparent hysteresis exhibits original features. We observe very long transient regimes before steady state, up to several hundreds of seconds. Furthermore, in steady state, the velocities are nonzero, meaning that the contact line is not strongly pinned to the surface defects, but are very small. The velocity of the contact line tends to vanish near the equilibrium contact angle. These observations are consistent with the thermally activated depinning theory that has been proposed to describe partial wetting systems on disordered substrates and suggest that a single physical mechanism controls both the hysteresis (or the pinning) and the motion of the contact line. The proposed analysis leads to the conclusion that the depinning activated energy is lower with pseudopartial wetting systems than with partial wetting ones, allowing the direct observation of the thermally activated motion of the contact line.

Heterogeneous nucleation in solutions: Generalized Gibbs’ approach

Heterogeneous nucleation in solutions on planar solid surfaces is modeled taking into account changes of the state parameters of the critical clusters in dependence on supersaturation. The account of the variation of the state parameters of the cluster phase on nucleation is performed in the framework of the generalized Gibbs' approach. A regular solution is chosen as a model for the analysis of the basic qualitative characteristics of the process. It is shown that, employing the generalized Gibbs approach, contact angle and catalytic activity factor for heterogeneous nucleation become dependent on the degree of metastability (supersaturation) of the solution. For the case of formation of a cluster in supersaturated solutions on a surface of low wettability (the macroscopic equilibrium contact angles being larger than 90°), the solid surface has only a minor influence on nucleation. In the alternative case of high wettability (for macroscopic equilibrium contact angles being less than 90°), nucleation is significantly enhanced by the solid surface. Effectively, the existence of the solid surface results in a significant shift of the spinodal to lower supersaturations as compared with homogeneous nucleation. Qualitatively, the same behavior is observed now near the new (solid surface induced) limits of instability of the solution as compared with the behavior near to the spinodal curve in the case of homogeneous nucleation.

Dynamic wetting in microfluidic droplet formation

The extent to which the carrier fluid wets the walls of a microchannel is crucial in the droplet formation process for segmented flow microfluidic applications and can be influenced by the use of surfac- tants. Surfactants dynamically modify the microchan- nel surface leading to stabilization of the two phase interface, affecting the droplet formation process. An experimental study of the influence of hydrophobic surfactant (Span 80) during the formation of water-in- oil droplets in a T-shaped microchannel geometry is presented and the wetting properties of the micro- channel walls were characterized. The range of data to be analyzed on the microscale is estimated from the macroscopic interfacial tension and contact angle mea- surements. The critical micelle concentration (CMC) level at the microscale was estimated by observing the trend of droplet length variation with concentration of surfactant in a microchannel. Microchannels used in this work were fabricated using softlithography meth- ods and bonded using a custom-made plasma bonding setup that does not require an ultra high vacuum cham- ber and hence saves the fabrication cost.

Density functional theory of electrowetting.

The phenomenon of electrowetting, i.e., the dependence of the macroscopic contact angle of a fluid on the electrostatic potential of the substrate, is analyzed in terms of the density functional theory of wetting. It is shown that electrowetting is not an electrocapillarity effect, i.e., it cannot be consistently understood in terms of the variation of the substrate-fluid interfacial tension with the electrostatic substrate potential, but it is related to the depth of the effective interface potential. The key feature, which has been overlooked so far and which occurs naturally in the density functional approach, is the structural change of a fluid if it is brought into contact with another fluid. These structural changes occur in the present context as the formation of finite films of one fluid phase in between the substrate and the bulk of the other fluid phase. The nonvanishing Donnan potentials (Galvani potential differences) across such film-bulk fluid interfaces, which generically occur due to an unequal partitioning of ions as a result of differences of solubility contrasts, lead to correction terms in the electrowetting equation, which become relevant for sufficiently small substrate potentials. Whereas the present density functional approach confirms the commonly used electrocapillarity-based electrowetting equation as a good approximation for the cases of metallic electrodes or electrodes coated with a hydrophobic dielectric in contact with an electrolyte solution and an ion-free oil, a significantly reduced tendency for electrowetting is predicted for electrodes coated with a dielectric which is hydrophilic or which is in contact with two immiscible electrolyte solutions.

Experimental and computational study of triple line shape and evolution on heterogeneous surfaces

Wetting of smooth, chemically heterogeneous surfaces was studied experimentally and computationally during the advancing and receding processes. The motion of the triple line is known to play an important role in determining the macroscopic contact angle due to its ability to be pinned at various defect locations on real surfaces. This effect is known to cause contact angle hysteresis. The shape of the triple line during these pinning/de-pinning events on various chemically heterogeneous surfaces was captured using an experimental and a computational technique. The experimental study employed a Modified Wilhelmy Plate Technique. The novelty in the current experimental setup lies in its ability to capture the microscopic triple line shape and its evolution in addition to measuring the local contact angles, which were both studied. The triple line shape was observed to be very sensitive to minor imperfections of the substrate. In addition, Surface Evolver was used to study the triple line shape computationally. Evolver was used to solve the complete three-dimensional problem by minimization of the total energy taking into consideration, both gravity and contact angle hysteresis. The studies showed that the temporal evolution of the triple line was significantly different during the advancing and receding processes based on the nature of the chemical heterogeneity. The results from the current work could be used in the design and fabrication of chemically heterogeneous surfaces for desired wetting applications.

Wetting of Macromolecules: From Linear Chain to Soft Colloid-Like Behavior

The ability to control the wetting properties of a polymeric liquid on a given surface is important for several emerging technological applications including protective coatings, lubricants and sensors. Here we show that star-shaped polystyrene (PS) molecules exhibit notably different wetting properties than their linear analogues of the same chemical structure and their wetting properties can be controlled through changes of their functionality f (number of arms per molecule). Unlike linear chains, the wetting of star-shaped macromolecules is determined by the competition between entropic forces. Wetting is enhanced due to reductions in the loss of entropy upon adsorption of the stars with increasing f; soft colloidal-like entropic repulsion effects suppress the ability of the stars to exhibit a high degree of surface adsorption and to efficiently pack, for sufficiently large values of f. This phenomenon is manifested in the existence of a minimum in the macroscopic contact angle and other related microscopic parameters embodied in the effective interface potential as a function of f.