Pressure dependence of the contact angle

When a liquid and its vapor contact a smooth, homogeneous surface, Gibbsian thermodynamics indicates that the contact angle depends on the pressure at the three-phase line of an isothermal system. When a recently proposed adsorption isotherm for a solid-vapor interface is combined with the equilibrium conditions and the system is assumed to be in a cylinder where the liquid-vapor interface can be approximated as spherical, the contact-angle-pressure relation can be made explicit. It indicates that a range of contact angles can be observed on a smooth homogeneous surface by changing the pressure at the three-phase line, but it also indicates that the adsorption at the solid-liquid interface is negative, and leads to the prediction that the contact angle increases with pressure. The predicted dependence of the contact angle on pressure is investigated experimentally in a system that has an independent mechanism for determining when thermodynamic equilibrium is reached. The predictions are in agreement with the measurements. The results provide a possible explanation for contact angle hysteresis.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

Amphiphilic co-networks with moisture-induced surface segregation for high-performance nonfouling coatings

Herein we report the design of a photocurable amphiphilic co-network consisting of perfluoropolyether and poly(ethylene glycol) segments that display outstanding nonfouling characteristics with respect to spores of green fouling alga Ulva when cured under high humidity conditions. The analysis of contact angle hysteresis revealed that the poly(ethylene glycol) density at the surface was enhanced when cured under high humidity. The nonfouling behavior of nonbiocidal surfaces against marine fouling is rare because such surfaces usually reduce the adhesion of organisms rather than inhibit colonization. We propose that the resultant surface segregation of these materials induced by high humidity may be a promising strategy for achieving nonfouling materials, and such an approach is more important than simply concentrating poly(ethylene glycol) moieties at an interface because the low surface energy has been maintained in our work.     

Electrical interaction between two cylinders with an ion-penetrable charged membrane in an oil/water interface

The electrical interaction between two long, parallel cylinders each is covered by an ion-penetrable charged membrane immersed in an oil/water interface is investigated. The effects of contact angle, radius of cylinder, and membrane thickness on the electrical interaction force are examined. The results of numerical simulation reveal that the following conditions lead to a greater electrical interaction force: (i) a larger contact angle, i.e. a larger fraction of a cylinder in the oil phase; (ii) a larger cylinder radius; and (iii) a thinner membrane. For a fixed ionic strength, the electrical interaction force is insensible to the type of electrolytes in the water phase, in general. However, if two cylinders are close enough, then the higher the valence of counterions the greater the electrical interaction force.     

Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events

We report a study of the orientations of nematic liquid crystals (LCs) in contact with peptide-modified, oligoethylene glycol-containing, self-assembled monolayers (SAMs). The SAMs were formed on gold films that were prepared by physical vapor deposition at an oblique angle of incidence. Two peptides were investigated: the optimized substrate for the Src protein kinase (IYGEFKKKC) and the synthetic equivalent of that peptide after kinase modification (IpYGEFKKKC). Polarization modulation-infrared reflectance absorbance spectroscopy (PM-IRRAS) was used to characterize the relative areal densities and orientations of these peptides at the interface. We conclude that the presence/absence of a phosphate group can influence the maximum packing density of immobilized peptide. We evaluated the orientations of the nematic liquid crystal 5CB in contact with these peptide-modified surfaces by using polarized microscopy. The time required for the nematic phase of 5CB to exhibit long-range orientational ordering (uniform alignment) was found to increase with increasing areal densities of immobilized peptide. We also found that the specific binding event between anti-phosphotyrosine IgG and the surface-immobilized phosphopeptide leads to an increase in the time required for the liquid crystal to achieve uniform anchoring (exceeding the experimentally accessible time scales). These results, when combined, suggest that the areal density and size of biomolecules at an interface can influence the time required for liquid crystals in contact with nanostructured surfaces to exhibit long-range orientational order. Finally, we illustrate the potential utility of this system by demonstrating that liquid crystals can be used to amplify and report protein binding events occurring on a spatially resolved peptide array.     

Using the meniscus in a capillary for small volume contact angle measurement in biochemical applications

The contact angle is a sensitive parameter often used to define wettability. With the increasing movement toward smaller liquid volumes in many biochemical applications, a key challenge lies in how to perform measurements in the retainer holding the reagent for rapid evaluation and limited material loss. Here, we report a simple and robust method to determine the contact angle of small volumes using the microscopic imaging of a capillary meniscus that requires only the radius and meniscus height information. An error analysis of the measurement finds the method to be highly accurate. We also uncovered that illumination delivered from the liquid end of the capillary lights up the interface, thereby facilitating the measurement.     

Physical properties of nanobubbles on hydrophobic surfaces in water and aqueous solutions

In recent years there has been an accumulation of evidence for the existence of nanobubbles on hydrophobic surfaces in water, despite predictions that such small bubbles should rapidly dissolve because of the high internal pressure associated with the interfacial curvature and the resulting increase in gas solubility. Nanobubbles are of interest among surface scientists because of their potential importance in the long-range hydrophobic attraction, microfluidics, and adsorption at hydrophobic surfaces. Here we employ recently developed techniques designed to induce nanobubbles, coupled with high-resolution tapping-mode atomic force microscopy (TM-AFM) to measure some of the physical properties of nanobubbles in a reliable and repeatable manner. We have reproduced the earlier findings reported by Hu and co-workers. We have also studied the effect of a wide range of solutes on the stability and morphology of these deliberately formed nanobubbles, including monovalent and multivalent salts, cationic, anionic, and nonionic surfactants, as well as solution pH. The measured physical properties of these nanobubbles are in broad agreement with those of macroscopic bubbles, with one notable exception: the contact angle. The nanobubble contact angle (measured through the denser aqueous phase) was found to be much larger than the macroscopic contact angle on the same substrate. The larger contact angle results in a larger radius of curvature and a commensurate decrease in the Laplace pressure. These findings provide further evidence that nanobubbles can be formed in water under some conditions. Once formed, these nanobubbles remain on hydrophobic surfaces for hours, and this apparent stability still remains a well-recognized mystery. The implications for sample preparation in surface science and in surface chemistry are discussed.     

Simulation of block copolymer stabilized nanoparticles in a two-solvent system

In this paper, by using Brownian Dynamics simulation, we investigate in general terms the behavior of a nanoparticle stabilized by a block copolymer in the presence of an oil-water interface. We investigate the probability of sticking to the interface, the density distribution of the copolymer across the interface and the area occupied by the stabilized nanoparticle at the interface. By using representative snapshots of the stabilized nanoparticle, derived from the density distribution, we find that the nanoparticle stabilized by a block copolymer, with the hydrophobic side of it tethered to the nanoparticle, prefers sitting at the oil-phase, and thus has a contact angle that is tested to be larger than 90 degrees for most of the cases, even if the hydrophobe content is less than 50%. Thus we find the architecture of a block-copolymer attachment to have a significant effect on the emulsion type that would result.     

Shape of the capillary meniscus around an electrically charged particle at a fluid interface: comparison of theory and experiment

Here, we consider in detail the problem of the shape of the capillary meniscus around a charged colloidal particle, which is attached to a fluid interface: oil/water or air/water. The meniscus profile is influenced by the electric field created by charges at the particle/nonpolar fluid boundary. We digitized the coordinates of points from the meniscus around silanized glass spheres (200-300 mum in radius) attached to the tetradecane/water interface. The theoretical meniscus shape is computed in three different ways that give numerically coincident results. It is proven that for sufficiently small particles the meniscus profile can be expressed as a superposition of pure electric and gravitational deformations. Special attention is paid to the comparison of theory and experiment. A procedure for data processing is developed that allows one to obtain accurate values of the contact angle and surface charge density from the fit of the experimental meniscus profile. For all investigated particles, excellent agreement between theory and experiment is achieved. The results indicate that the electric field gives rise to an interfacial deformation of medium range and considerable amplitude.     

Characterizing the surface quality and droplet interface shape for microarray plates

The variation in the surface quality of microarray plates was examined by measuring the contact angles of 480 droplets on five microarray plates. It was found that the measured contact angle did not accurately predict the droplet shape for moderate Bond numbers (~0.5 ≤ N(B) ≤ 5). By defining an apparent contact angle using the ratio of the contact radius to the height, the variance in the predicted interface shape decreased by greater than a factor of 3 for both local and globally averaged characteristics. The error in the predicted droplet height was also reduced by 3 orders of magnitude.     

Limiting conditions for applying the spherical section assumption in contact angle estimation

The shape of liquid drops on solid surfaces deviates from the spherical as tension decreases and gravity effects start affecting the drop shape. This paper attempts to define this deviation and estimates the dimensionless Eotvos number limits above which the deviation becomes "significant." The use of these limiting values can facilitate estimation of contact angle in the following manner. It is well known that the equilibrium contact angle made by a liquid drop on a solid surface can be estimated from measurements of two drop parameters. These parameters can be any two chosen from the drop volume, height, and wetted radius. In case the effect of gravity on the drop shape is negligible, simple algebraic relations derived from the spherical section assumption exist, from which the contact angle can be estimated. In systems where the "spherical section" assumption is invalid, the Laplace equation for the drop shape has been solved numerically with any two of the above parameters as the constraints, to obtain the contact angle. In this paper, Eotvos numbers at which the deviation of the drop profile from the spherical is significant enough to result in contact angle deviation of 1 degrees are estimated. The limiting values of Eotvos number, expressed as a function of the original contact angle made by the spherical profile, are obtained by solving the Laplace equation for the drop shape with the drop volume and wetted radius constraints for decreasing values of Interfacial tension. These limiting values are also estimated for different drop sizes and for cases where the drop phase is heavier (sessile) and lighter (buoyant) than the surrounding fluid. The independence of the Eotvos number estimates from the sign of the density difference as well as the drop size is shown. These Eotvos number limits can be used to check if the spherical section assumption, with the resulting simple algebraic relations, can be used for contact angle estimation and other shape-related analysis for a system.     

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.     

Calomel reference electrode in propylene carbonate

Measurements of the contact angle of an air bubble against thin films of silver iodide in an electrolyte solution have been made, using the captive bubble technique, as a function of pAg. The receding contact angle reached its maximum value at a pAg=5.4±0.2. This pAg value coincides closely with the isoelectric point of the silver iodide solution interface. A thermodynamic analysis is given which relates the variation of contact angle to the variation of concentration of potential determining ions and surface charge density.     

Anisotropic drop morphologies on corrugated surfaces

The spreading of liquid drops on surfaces corrugated with micrometer-scale parallel grooves is studied both experimentally and numerically. Because of the surface patterning, the typical final drop shape is no longer spherical. The elongation direction can be either parallel or perpendicular to the direction of the grooves, depending on the initial drop conditions. We interpret this result as a consequence of both the anisotropy of the contact line movement over the surface and the difference in the motion of the advancing and receding contact lines. Parallel to the grooves, we find little hysteresis due to the surface patterning and that the average contact angle approximately conforms to Wenzel's law as long as the drop radius is much larger than the typical length scale of the grooves. Perpendicular to the grooves, the contact line can be pinned at the edges of the ridges, leading to large contact angle hysteresis.     

Wetting behavior of spherical nanoparticles at a vapor-liquid interface: a density functional theory study

The wetting behavior of spherical nanoparticles at a vapor-liquid interface is investigated by using density functional theory, and the line tension calculation method is modified by analyzing the total energy of the vapor-liquid-particle equilibrium. Compared with the direct measurement data from simulation, the results reveal that the thermodynamically consistent Young's equation for planar interfaces is still applicable for high curvature surfaces in predicting a wide range of contact angles. The effect of the line tension on the contact angle is further explored, showing that the contact angles given by the original and modified Young's equations are nearly the same within the region of 60° < θ < 120°. Whereas the effect is considerable when the contact angle deviates from the region. The wetting property of nanoparticles in terms of the fluid-particle interaction strength, particle size, and temperature is also discussed. It is found that, for a certain particle, a moderate fluid-particle interaction strength would keep the particle stable at the interface in a wide temperature range.     

Interfacial oil droplets

Very small, discrete oil droplets can form at the solid-liquid interface. We demonstrate this effect through formation of decane droplets at the interface between an aqueous ethanol solution and silicon wafers that have been made hydrophobic through self-assembly of octadecyltrichlorosilane (OTS). The droplets have a lens-like shape; the shape is approximately a spherical cap with a contact angle < 25 degrees. The heights of the droplets are about 2-50 nm, and diameters at the three-phase boundary are about 100-600 nm in 25% ethanol solution. The size and contact angle can be varied by changing the ethanol concentration. The contact angle of the very small droplets (height < 20 nm) is similar to the contact angle of macroscopic droplets (height approximately equal to 1 mm), so the line tension is very small. The droplets are only stable for a few hours: they gradually lose mass, presumably through Ostwald ripening. The drop perimeter is not pinned during ripening but retreats across the solid. We form the droplets by direct adsorption from an emulsion; evidence for adsorption is obtained by comparing the drop volumes in bulk to the volumes at the interface. The droplet sizes are obtained by dynamic light scattering and atomic force microscopy.     

Contact angles in relation to emulsions stabilised solely by silica nanoparticles including systems containing room temperature ionic liquids

We report measured and calculated oil-ionic liquid, water-ionic liquid and oil-water contact angles on silica surfaces which have been hydrophobised to different extents by silanisation. Based on the idea that the contact angle formed by a liquid-liquid interface with a particle adsorbed at that interface is a key determinant of the strength of particle adsorption and the tendency of the adsorbed particle film to curve, we correlate the contact angle data with the phase inversion points and stabilities of the corresponding particle-stabilised emulsions.     

Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.     

Analysis of the gas states at a liquid/solid interface based on interactions at the microscopic level

The states of gas accumulated at the liquid/solid interface are analyzed on the basis of the continuum theory, in which the Hamaker constant is used to describe the long-range interaction at the microscopic scale. The Hamaker constant is always negative, whereas the "gas" spreading coefficient can be either negative or positive. Despite the complexity of gas, including that the density profile may not be uniform due to absorption on both solid and liquid surfaces, we predict three possible gas states at the liquid/solid interface, that is, complete "wetting", partial "wetting", and pseudopartial "wetting". These possible gas states correspond, respectively, to a gas pancake (or film) surrounded by a wet solid, a gas bubble with a finite contact angle, and a gas bubble(s) coexisting with a gas pancake. The typical thickness of the gas pancakes is at the nano scale within the force range of the long-range interaction, whereas the radius of the gas bubbles can be large. The state of a gas bubble(s) coexisting with a gas film is predicted theoretically for the first time. Our theoretical results can contribute to the development of a unified picture of gas nucleation at the liquid/solid interface.     

Amphiphilic silica nanoparticles at the decane-water interface: insights from atomistic simulations

The properties of 3 nm-diameter silica nanoparticles with different surface chemistry were systematically investigated at the decane-water interface using molecular dynamics simulations. Our results show that the decane-water interfacial tension is not much influenced by the presence of the nanoparticles. The three-phase contact angle increases with nanoparticle surface hydrophobicity. Contact angles observed for the nanoparticles at 300 and at 350 K differ very little. The contact angle of the nanoparticle with randomly dispersed hydrophobic groups is smaller than that observed in Janus nanoparticles of equal overall surface chemistry composition. The energy necessary to desorb Janus nanoparticles from the interface is usually higher than that required to desorb the corresponding homogeneous nanoparticles. Desorption from the interface into the aqueous phase is preferred over that into the organic phase for all except one of the nanoparticles considered. Structural and dynamic properties including nanoparticle rotational relaxation, solvent density profiles, and solvent residence autocorrelation functions near the nanoparticles are also presented. The data are useful for designing Pickering emulsions.