A Novel Method for Surface Free-Energy Determination of Powdered Solids

Interfacial solid/liquid interactions play a crucial role in wetting, spreading, and adhesion processes. In the case of a flat solid surface, contact angle measurements are commonly utilized for the determination of the solid surface free energy and its components. However, if such a surface cannot be obtained, then the contact angle can not be measured directly. Usually methods based on imbibition of probe liquids into a thin porous layer or column are applied. In this paper a novel method, also based on the capillary rise, is proposed for the solid surface free-energy components determination. Actually, it is a modification of the thin column wicking method; similar theoretical background can be applied together with that appropriate for the capillary rise method of liquid surface tension determination. The proposed theoretical approach and procedure are verified by using single glass capillaries, and then alumina and ground glass powders were used for the method testing. Thus obtained surface free-energy components for these solids, for both glass and alumina, agree well with the literature values.     

Measurement of the surface tension of liquid marbles

The capillary rise and Wilhelmy plate methods have been used to study the "surface tension" of water marbles encapsulated with polytetrafluoroethylene (PTFE) powders of 1-, 35-, and 100-μm particle size. With the capillary rise technique, a glass capillary tube was inserted into a water marble to measure the capillary rise of the water. The Laplace pressure exerted by the water marble was directly measured by comparing the heights of the capillary rise from the marble and from a flat water surface in a beaker. An equation based on Marmur's model was proposed to calculate the water marble surface tension. This method does not require the water contact angle with the supporting solid surface to be considered; it is therefore a simple but efficient method for determining liquid marble surface tension. The Wilhelmy method was used to measure the surface tension of a flat water surface covered by PTFE powder. This method offers a new angle for investigating liquid marble shell properties. A discussion on the nature and the realistic magnitude of liquid marble surface tension is offered.     

Thermal healing of scratches and determination of solid surface tension of selenium

The healing of scratches on the surface of vitreous selenium was observed over a period of nine weeks, and from the data the solid surface tension of vitreous Se is estimated to be (100 ± 20) dyne/cm at 38.8°C, about the same as that of the liquid at the melting point. This value is three times as large as the critical surface tension determined from contact angle measurements, which indicates that for vitreous Se in contact with organic liquids, the solid—liquid interfacial tension is about two-thirds as much as the solid surface tension. The present method of measurement can probably be used to determine the solid surface tension of other polymers, and by measuring the healing of scratches on a solid immersed in a liquid the method could be used to determine the solid—liquid interfacial tension.     

Low‐rate dynamic contact angles on poly(methyl methacrylate/ethyl methacrylate, 30/70) and the determination of solid surface tensions

Low‐rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/ethyl methacrylate, 30/70) P(MMA/EMA, 30/70) copolymer were measured by an automated axisymmetric drop shape analysis‐profile (ADSA‐P). It was found that five liquids yield nonconstant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining seven liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension (i.e., γ_l|Kv cos θ depends only on γ_l|Kv for a given solid surface or solid surface tension). This contact angle pattern is in harmony with those from other methacrylate polymer surfaces previously studied.^45,50 The solid–vapor surface tension calculated from the equation‐of‐state approach for solid–liquid interfacial tensions¹⁴ is found to be 35.1 mJ/m², with a 95% confidence limit of ± 0.3 mJ/m², from the experimental contact angles of the seven liquids. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2039–2051, 1999     

Silicon-Modified Carbohydrate Surfactants V: The Wetting Behaviour of Low-Molecular-Weight Siloxane,Carbosilane, Silane and Polysilane Precursors on Low-Energy Surfaces

The surface tensions, wetting tensions, contact angles and solid/liquid interfacial tensions of defined siloxanes as well as those of analogous carbosilanes, polysilanes and neopentyl substituted silanes were determined. The wetting experiments were carried out on a glass plate coated with perfluoroalkyl methacrylate (FC 722^®). The siloxanes possess the lowest surface tensions. Due to the presence of oxygen atoms in the siloxane backbone, a donor–acceptor portion (γ^+/−_lv) of the surface tension of about 1–2 mN/m was determined. The solid/liquid interfacial tension also contains a donor–acceptor portion (γ^+/−_sl). Its value is almost identical to that of γ^+/−_lv. The γ^+/−_sl differences between individual molecules of the same surface tension are responsible for contact angle differences of up to 4°. © 1997 John Wiley & Sons, Ltd.     

Physical significance of contact angles

Summary The physical significance of contact angles has been interpreted on the basis of a model derived from known surface energy relationships. The degrees of non-spreading and spreading have been expressed in terms of the magnitude of contact angles. On the basis of the physical picture, hysteresis of contact angle has been calculated from the experimental values of equilibrium contact angle and surface tension of the liquid. It has been suggested that it is not necessary to assume that hysteresis of contact angles is due to surface roughness of solids. The picture also explains why apparent contact angle on a non-flat solid surface is more than that on a flat solid.With 2 figures and 1 table     

Solid/liquid interfacial tension as a tool to study stability of lysozyme on adsorption to solid surfaces

This work proposes the use of solid/liquid interfacial tension to study the stability of adsorbed lysozyme films on a solid surface using the contact angle of a liquid at the three phase contact line, in the presence of a denaturant, urea.Results suggest a direct correlation between this method with a standard technique like the fluorescence emission spectra and is measured with the same observable error as in the spectral methods. Further the technique provides a simple and direct handle to evaluate the homogeneity and degree of polarity of protein films on solid surfaces.     

Small solid particles and liquid lenses at fluid/fluid interfaces

The behaviour of small solid particles and liquid droplets at fluid interfaces is of wide interest, in part because of the roles they play in the stability of foams and emulsions. Here we focus on solid particles at liquid interfaces, both singly and in highly structured monolayers. We briefly mention small oil lenses on water in connection with the determination of line tension, τ. Particles are surface-active in the sense that they often adhere quite strongly to liquid surfaces, although of course they are not usually amphiphilic. The three-phase contact line around a particle at an interface is associated with an excess free energy resulting in a tendency of the line to contract (positive τ, which is a 1D analogue of surface tension) or to expand (negative τ). Positive line tension acts so as to push the contact angle of a particle with the fluid interface further away from 90°, i.e. to force the particle towards the more “wetting” of the two bulk phases. It also leads to activation barriers to entry and departure of particles from an interface. The behaviour of particle monolayers at octane/water interfaces is also discussed . It is found that, for monodisperse spherical polystyrene particles containing ionisable sulphate groups at the surface, highly ordered monolayers are formed. This appears to result from very long range electrostatic repulsion mediated through the oil phase. Surface pressure–surface area isotherms are discussed for particle monolayers and it is shown, using light microscopy, that at monolayer “collapse” particles are not expelled from the monolayers but rather the monolayer folds, remaining intact. This has an important bearing on methods, involving the use of the Langmuir trough, for the experimental determination of contact angles and line tensions in particulate systems. Received: 18 July 1999/Accepted: 30 August 1999     

Electrowetting of nonwetting liquids and liquid marbles

Transport of a water droplet on a solid surface can be achieved by differentially modifying the contact angles at either side of the droplet using capacitive charging of the solid-liquid interface (i.e., electrowetting-on-dielectric) to create a driving force. Improved droplet mobility can be achieved by modifying the surface topography to enhance the effects of a hydrophobic surface chemistry and so achieve an almost complete roll-up into a superhydrophobic droplet where the contact angle is greater than 150 degrees . When electrowetting is attempted on such a surface, an electrocapillary pressure arises which causes water penetration into the surface features and an irreversible conversion to a state in which the droplet loses its mobility. Irreversibility occurs because the surface tension of the liquid does not allow the liquid to retract from these fixed surface features on removal of the actuating voltage. In this work, we show that this irreversibility can be overcome by attaching the solid surface features to the liquid surface to create a liquid marble. The solid topographic surface features then become a conformable "skin" on the water droplet both enabling it to become highly mobile and providing a reversible liquid marble-on-solid system for electrowetting. In our system, hydrophobic silica particles and hydrophobic grains of lycopodium are used as the skin. In the region corresponding to the solid-marble contact area, the liquid marble can be viewed as a liquid droplet resting on the attached solid grains (or particles) in a manner similar to a superhydrophobic droplet resting upon posts fixed on a solid substrate. When a marble is placed on a flat solid surface and electrowetting performed it spreads but with the water remaining effectively suspended on the grains as it would if the system were a droplet of water on a surface consisting of solid posts. When the electrowetting voltage is removed, the surface tension of the water droplet causes it to ball up from the surface but carrying with it the conformable skin. A theoretical basis for this electrowetting of a liquid marble is developed using a surface free energy approach.     

Line tension and its influence on droplets and particles at surfaces

In this review we examine the influence of the line tension τ on droplets and particles at surfaces. The line tension influences the nucleation behavior and contact angle of liquid droplets at both liquid and solid surfaces and alters the attachment energetics of solid particles to liquid surfaces. Many factors, occurring over a wide range of length scales, contribute to the line tension. On atomic scales, atomic rearrangements and reorientations of submolecular components give rise to an atomic line tension contribution τ_atom (～1 nN), which depends on the similarity/dissimilarity of the droplet/particle surface composition compared with the surface upon which it resides. At nanometer length scales, an integration over the van der Waals interfacial potential gives rise to a mesoscale contribution |τ_vdW| ～ 1–100 pN while, at millimeter length scales, the gravitational potential provides a gravitational contribution τ_grav ～ +1–10 μN. τ_grav is always positive, whereas, τ_vdW can have either sign. Near wetting, for very small contact angle droplets, a negative line tension may give rise to a contact line instability. We examine these and other issues in this review.     

Nanodrop on a nanorough solid surface: density functional theory considerations

The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.     

Contact angle interpretation in terms of solid surface tension

Recent experimental (low-rate) dynamic contact angles for 14 solid surfaces are interpreted in terms of their solid surface tensions. Universality of these experimental contact angle patterns is illustrated; other reasons that can cause data to deviate from the patterns are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming solid surface tension is constant for one and the same solid surface, experimental contact angle patterns are employed to deduce a functional relationship to be used in conjunction with the Young equation to determine solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelot’s rule together with experimental data; essentially constant solid surface tension values are obtained, independent of liquid surface tension and molecular structure. A new combining rule is also derived based on an expression similar to one used in molecular theory; such a combining rule should allow a better understanding of the molecular interactions between unlike solid–liquid pairs.     

Validity of the "sharp-kink approximation" for water and other fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.     

小角躺滴法测定低界面张力

在测定界面张力,特别是测定低界面张力的各种方法中,躺滴法占有相当重要的位置。但一般的躺滴法都要求获得赤道半径(图1中的x_e)数据.故躺滴与基底之间的接触角必须大于90°.这在低界面张力体系中常常难以实现,致使躺滴法的应用受到限制。本文提出一种新的躺滴法,它不依赖于接触角的大小,只需测定躺滴轮廓线上两个相关点的坐标,根据所给数值表即可计算出界面张力,从而为躺滴法应用于低界面张力,特别是     

Static and Dynamic Wetting Behavior of Triglycerides on Solid Surfaces

Triglyceride wetting properties on solid surfaces of different hydro-phobicities were investigated using three different methods, namely, the sessile drop method for static contact angle measurements, the Wilhelmy method for dynamic contact angle measurements, and the captive bubble method to investigate thin triglyceride film stability. For solid surfaces having a surface free energy higher than the surface tension of triglycerides (tributyrin, tricaprylin, and triolein), a qualitative correlation was observed between wetting and solid/triglyceride relative hydrophobicities. On surfaces presenting extreme hydrophobic or hydrophilic properties, medium-chain triglycerides had a behavior similar to that of long-chain unsaturated ones. On a high-energy surface (glass), tricaprylin showed an autophobic effect subsequent to molecular adsorption in trident conformation on the solid, observed with the three methods. Thin triglyceride films between an air bubble and a solid surface were stable for a short time, for solids with a surface free energy larger than the triglyceride surface tension. If the solid surface had a lower surface free energy, the thin film collapsed after a time interval which increased with triglyceride viscosity. Copyright 2000 Academic Press.     

Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface

A model according to which contact-angle hysteresis arises as the result of a random distribution of irregularities on the solid surface is investigated on the basis of probability theory. An estimate is obtained of the mathematical expectation of the number of stable equilibria when the effective angle between the liquid-gas surface and the solid surface with which the liquid is in contact deviates from the value, say theta(0), which would obtain if the solid surface were uniform, i.e., free from irregularities. It is found that when the effective contact angle deviates from theta(0) by less than a critical value, then the expected number of stable equilibria increases exponentially with the length of the contact line; therefore such a contact angle can occur under static conditions. But if the deviation of the contact angle from theta(0) exceeds the critical value, then the expected number of stable equilibria decreases exponentially with the length of the contact line, so a stable equilibrium is not possible for a macroscopic length of the contact line. The method is applicable only if the random deviations of the spreading power (defined as the solid-gas surface tension minus the sum of the liquid-gas and liquid-solid surface tensions) from its average are sufficiently small. It is found that the critical deviation of the contact angle from theta(0) is, apart from a slowly varying logarithmic factor, proportional to H(2)rho(s), where H is a measure of the amplitude of the surface irregularities and rho(s) is the surface density (i.e., number per unit area) of the irregularities. This qualitative feature agrees with the results previously obtained by several other authors, and, moreover, there is a surprisingly close agreement of the proportionality factor with the results of some earlier work in which the method of statistical analysis was much less elaborate than here. The effect of the logarithmic factor is to make the critical deviation of the contact angle increase more slowly than the first power of H(2)rho(s), and this is also in qualitative agreement with some earlier work. Copyright 2000 Academic Press.     

Determining the contact angle between liquids and cylindrical surfaces

One of the simplest methods of measuring the quantities for estimating the adhesion properties of materials (i.e., the adhesion work, the surface energy, and the interfacial tension between certain liquids and a surface) requires the determination of the contact angle between the liquid and the surface. In the case of plane surfaces the determination of the drop dimensions makes it possible to calculate the contact angle by the sessile drop method, but in the case of cylindrical surfaces (such as the monofilaments), several methods were developed to improve the accuracy of the contact angle measurements. This paper presents a comprehensive method for precise evaluation of the contact angle between liquid drops and monofilaments by establishing a differential equation describing the drop contour. This equation makes it possible to accurately compute the contact angle using the dimensions of the drop. A comparison of the values of the contact angle calculated by our method and those obtained by other approaches is made. We applied our method in the case of polyamide-6 monofilaments treated using dielectric barrier discharge, knowing their medical applications in surgical sutures.     

Prediction of solid-fluid interfacial tension and contact angle

Two simple equations have been developed using the lattice theory and the regular solution assumption to predict the solid-vapor and solid-liquid interfacial tension. The required parameters are the liquid critical temperature and volume, the solid melting temperature and the molar volume of liquid and solid compounds. To confirm the models, the predicted solid-fluid interfacial tension values have been used to predict the contact angle of the liquid drop on the solid surface applying Young's equation. Agreement of the predicted contact angle with the experimental data reveals the reliability of the developed models.     

The Surface Energy and Contact Angles of a Liquid Foam

A liquid foam can be regarded as a single fluid with a characteristic "surface tension". This property is calculated for two- and three-dimensional ordered and disordered foams using a broken bond approach. The contact angle of a foam with a solid or a liquid substrate is also calculated from the energies of the bubbles in contact with the substrate. Experiments were carried out in which the contact angles of foams were measured, with reasonable agreement with the predictions. Copyright 2001 Academic Press.     

A method for correcting the contact angle from the θ/2 method

The θ/2 method, a widely used technique on measuring the contact angle of a sessile drop, assumes that the drop profile is part of a sphere. However, the shape profile of a sessile drop is governed by the Young–Laplace equation and is different from a sphere, especially for drops with a large bound number (e.g. large volume or small surface tension). The spherical assumption, therefore, causes errors on evaluating the contact angles. The deviation of contact angle from the θ/2 method is evaluated from a theoretical calculation in this work. A simple means is given for correcting the measurement error. The corrected angle results from the drop volume, surface tension, liquid density and the contact angle from θ/2 method. An algorithm for finding the correct contact angle without knowing the density and surface tension is also given. At the end, two examples of pendant drops are given for the illustration.