Determination of line tension for systems near wetting

Contact angle measurements for three n-alkanes, heptane, octane, and nonane, on two different self-assembled surfaces (SAM) are reported as a function of drop size. These liquids all formed low contact angles (below 20 degrees ); the measurements were performed using an accurate method for systems with low contact angle, ADSA-D. The observed drop size dependence of the contact angles was interpreted using the modified Young equation. It was concluded that the observed drop size dependence of contact angles was due to line tension. The choice of systems also provided the opportunity to examine the behavior of the line tension for systems near wetting (i.e., low contact angles). It was determined that the line tension is positive and ranges from below 10(-7) to just below 10(-6) J/m for the systems studied; the observations suggested that the line tension decreases as the contact angle decreases and likely vanishes at complete wetting.     

Molecular simulation of fluid-solid interfaces at nanoscale

The equilibrium states of vapor and liquid coexistent phases in contact with a solid surface are studied at the nanoscale by molecular dynamics simulations for a temperature close to the fluid triple point. The characteristics of the solid-fluid interfaces are determined when the interaction strength between the fluid and the solid varies in order to go from a situation of complete drying to that of complete wetting. From the vapor-liquid density profiles of liquid drops lying on the substrate surface or menisci of liquid films confined in slit pores, the contact angles made by the vapor-liquid interface with the solid are computed. The angle values are similar for the drops and the films. They are also in good qualitative agreement with the estimates obtained through the Young's relation from the surface tensions associated with the vapor-solid, liquid-solid, and vapor-liquid interfaces. However, at this scale, the uncertainties inherent to the angle computation and, to a lesser extent, to size effects seem to preclude that the quantitative agreement between the angle estimates obtained from the interface geometry and calculated from the Young's relation can be better than few degrees.     

Adsorption of acicular particles at liquid-fluid interfaces and the influence of the line tension

In this paper, the adsorption energy of an acicular (prolate and cylindrical) particle onto a liquid-fluid interface and the effect of the line tension are investigated. The results show that, without line tension, acicular particles always prefer to lie flat in the plane of the interface. However, line tension plays a significant role in determining the adsorption of an acicular particle. First, the line tension creates an energy barrier for the adsorption of particles onto an interface. The planar configuration has a larger energy barrier due to the longer contact line. Therefore, the particles prefer to enter the interface in a homeotropic configuration and then rearrange to a planar configuration or an oblique configuration with a small tilt angle. Second, for prolate particles, an energy maximum occurs at some tilt angles when the line tension is large. Therefore, once the prolate particle is adsorbed on the interface in a homeotropic configuration or with a larger tilt angle, it must conquer an energy barrier to rearrange to a planar configuration. For cylindrical particles, when the line tension is higher, the planar configuration will not be the most energy-favorable configuration. The cylindrical particles prefer to stay in the interface with a small tilt angle.     

Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

The evaporation of sessile drops at reduced pressure is investigated. The evaporation of water droplets on aluminum and PTFE surfaces at reduced pressure was compared. It was found that water droplets on an aluminum surface exhibit a 'depinning jump' at subatmospheric pressures. This is when a pinned droplet suddenly depins, with an increase in contact angle and a simultaneous decrease in the base width. The evaporation of sessile water droplets with a nonionic surfactant (Triton X-100) added to an aluminum surface was then studied. The initial contact angle exhibited a minimum at 0.001 wt% Triton X-100. A maximum in the evaporation rate was also observed at the same concentration. Droplets with low surfactant concentrations are found to exhibit the 'depinning jump.' It is thought that the local concentration of the surfactant causes a gradient of surface tension. The balance at the contact angle is dictated by complex phenomena, including surfactant diffusion and adsorption processes at interfaces. Due to the strong evaporation near the triple line, an accumulation of the surfactant will lead to a surface tension gradient along the interface. The gradient of surface tension will influence the wetting behavior (Marangoni effect). At low surfactant concentrations the contact line depins under the strong effect of surface tension gradient that develops spontaneously over the droplet interface due to surfactant accumulation near the triple line. The maximum evaporation rate corresponds to a minimum contact angle for a pinned droplet.     

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     

Theoretical study of the three-phase contact line and its tension in adsorbed colloid-polymer mixtures

We perform a theoretical study of the three-phase contact line and the line tension in an adsorbed colloid-polymer mixture near a first-order wetting transition, employing an interface displacement model. We use a simple free-energy functional to describe a colloid-polymer mixture near a hard wall. The bulk phase behavior and the substrate-adsorbate interaction are modeled by the free-volume theory for ideal polymers. The large size of the colloidal particles and the suppression of the van der Waals interaction by optical matching of colloid and solvent justify the planar hard wall model for the substrate. Following the Fisher-Jin scheme, we derive from the free-energy functional an interface potential V(l) for these mixtures. For a particle diameter of 10-100 nm, the calculations indicate a line tension tau approximately 10(-12)-10(-13) N at room temperature. In view of the ultralow interfacial tension in colloid-polymer mixtures, gamma approximately 10(-7) Nm, this leads to a rather large characteristic length scale taugamma in the micrometer range for the three-phase contact zone width. In contrast with molecular fluids, this zone could be studied directly with optical techniques such as confocal scanning laser microscopy.     

Status of the three-phase line tension: a review

From a thermodynamic point of view, the concept of line tension is on solid ground; it is well recognized and defined. There is a notion in the literature that there is little consensus with regards to magnitude or sign of line tension. Partly, inappropriate comparisons of line tension values may have contributed to the current uncertainty, especially some between theoretical and experimental values. A wide range of reported line tension values may not necessarily be a result of conflicting findings, but it may reflect the diversity of systems studied. However, differences among similar approaches and systems observed are sometimes caused by one or several of the following factors: difficulties in sample preparation, poor experimental techniques, non-equilibrium, or conceptual and theoretical difficulties and oversimplifications. It is important to clearly establish the magnitude and sign of line tension as it may determine its relevance to technological applications such as microfluidic systems.

This review has examined a wide range of recent and past studies on the subject of line tension. The review classifies line tension studies into theoretical and experimental; it further groups the studies into liquid–liquid–vapor and solid–liquid–vapor systems for each category. The review provides a comparison between similar studies in an attempt to clarify the current status of line tension research. The majority of theoretical line tension studies (excluding the near wetting studies) have estimates for line tension of about 10⁻¹⁰ N; however, for special cases, values as high as 10⁻⁶ N are also reported. There is less consensus regarding the sign for the line tension as theoreticians often assert that line tension can have either a positive or a negative sign. In experimental studies of liquid–liquid–vapor systems the majority of studies reported positive values for line tension; for film studies, the magnitude of line tension reported was between 10⁻⁹ and 10⁻⁷ N, whereas for studies of liquid lens values as high as 10⁻⁶ N were also reported. The clear majority of studies for solid–liquid–vapor systems reported a positive sign for line tension. In studies involving particles, line tension values ranged from 10⁻⁹ to 10⁻⁶ N. Studies using drop size dependence of contact angles reported values mostly in the span of 10⁻⁹–10⁻⁶ N; however, a clear majority of the reported values fell in the higher end of the above range. The special topic of line tension near wetting was also studied. While the interface displacement model appears to have brought about consensus with respect to certain aspects of line tension behavior near wetting, this model maybe still too phenomenological to be satisfactory from a more fundamental standing. Experimentalists have just begun studying line tension for systems near wetting, this is encouraging, but more comprehensive studies are needed.     

Contact angle hysteresis of microbead suspensions

Microbead suspensions are often used in microfluidic devices for transporting biomolecules. An experimental investigation on the wettability of microbead suspension is presented in this study. The variation in the surface tension and the equilibrium contact angle with the change in the volume fraction of the microbead is presented here. The surface tension of the microbead suspension is measured with the pendant drop technique, whereas the dynamic contact angle measurements, i.e., advancing and receding contact angles, are measured with the sessile drop technique. An equilibrium contact angle of a suspension with particular volume fraction is determined by computing an average over the measured advancing and receding contact angles. It is observed that the surface tension and the equilibrium contact angle determined from advancing and receding contact angles vary with the magnitude of the microbeads volume fraction in the suspension. A decrease in the surface tension with an increase in the volume fraction of the microbead suspension is observed. The advancement and the recession in contact line for dynamic contact angle measurements are achieved with the motorized dosing mechanism. For microbead suspensions, the advancement of the contact line is faster as compared to the recession of the contact line for the same flow rate. The presence of microbeads assists in the advancement and the recession of the contact line of the suspension. A decrease in the equilibrium contact angles with an increase in the microbead suspension volume fraction is observed. Inclusion of microbeads in the suspension increases the wetting capability for the considered combination of the microbead suspension and substrate. Finally, empirical correlations for the surface tension and the contact angle of the suspension as a function of microbead volume fraction are proposed. Such correlations can readily be used to develop mechanistic models for the capillary transport of microbead suspensions related to LOC applications.     

Orientation of a nanocylinder at a fluid interface

A nanocylinder placed on a fluid interface can assume an end-on or side-on orientation, or it can immerse itself in the surrounding bulk phases. Any of these orientations can satisfy a mechanical force balance when the particle is small enough that gravitational effects are negligible. The orientation is determined by the surface energies of the fluid-solid, fluid-vapor, and vapor-solid surfaces. A comparison of the energy of each state allows phase diagrams to be defined in terms of the scaled aspect ratio x=2L/pir and the contact angle thetao, where L and r denote the nanocylinder length and radius, respectively. Line tension can also influence the orientations by changing the equilibrium contact angle theta and by increasing the energetic cost of the contact line. Phase diagrams accounting for positive line tensions Sigma are also constructed. These phase diagrams can be divided into two classes. In the first, over some range of x and Sigma, nanocylinders can be driven from side-on to end-on orientations with increasing Sigma. This transition terminates at a triple point where the side-on, end-on, and immersed energies are the same. In the second class, there is no triple point and, for a range of Sigma values, nanocylinders of all aspect ratios x prefer an end-on orientation. In all cases, for high enough Sigma, line tension drives a wetting transition similar to that already noted in the literature for spherical particles. The zero line tension predictions are compared favorably to experiment, in which functionalized gold nanowires made by template synthesis are spread at aqueous-gas interfaces, immobilized using a gel-fixation technique, and observed by scanning electron microscopy. The small aspect ratio particles (disks) were in an end-on configuration, while the longer nanowires were in a side-on orientation, in agreement with the theory.     

Surface functionalization of SBA-15 and a nonordered mesoporous silica with a 1,4-diazabicyclo[2.2.2]octane derivative: study of CuCl2 adsorption from ethanol solution

The equilibrium position of a spherical or prolate spheroidal particle resembling a needle floating at the interface between two immiscible fluids is discussed. A three-dimensional meniscus attached to an a priori unknown contact line at a specified contact angle is established around the particle, imparting to the particle a capillary force due to surface tension that is balanced by the buoyancy force and the particle weight. An accurate numerical solution for a floating sphere is obtained by solving a boundary-value problem, and the results are compared favorably with an approximate solution where the effect of the particle surface curvature is ignored and the elevation of the contact line is computed using an analytical solution for the meniscus attached to an inclined flat plate. The approximate formulation is applied locally around the nearly planar elliptical contact line of a prolate spheroid to derive a nonlinear algebraic equation governing the position of the particle center and the mean elevation of the contact line. The effect of the fluid and particle densities, contact angle, and capillary length is discussed, and the shape of the contact line is reconstructed and displayed from the local solution.     

苄基取代甜菜碱对聚四氟乙烯表面润湿性的影响

利用座滴法研究了两性离子表面活性剂苄基取代烷基羧基甜菜碱(BCB)和苄基取代烷基磺基甜菜碱(BSB)在聚四氟乙烯(PTFE)表面上的润湿性质,考察了表面活性剂浓度对接触角的影响趋势,并讨论了粘附张力、固-液界面张力和粘附功的变化规律.研究发现,在低浓度时,表面活性剂通过疏水作用吸附到PTFE表面,疏水链苄基取代支链化使其在固-液界面上的吸附明显低于气-液界面,接触角在很大的范围内保持不变.当体相浓度增加到大于临界胶束浓度(cmc)时, BCB和BSB分子在固-液界面上继续吸附,分子逐渐直立,造成PTFE-液体之间的界面张力(γ_SL)进一步降低,表面亲水性增加,接触角随浓度增加明显降低;另一方面, BSB由于具有较大的极性头,在高浓度时空间阻碍作用明显,导致其对PTFE表面润湿性改变程度小于BCB.     

Estimation of line tension and contact angle from heterogeneous nucleation experimental data

Using the classical nucleation theory corrected with line tension and experimental data of heterogeneous nucleation of n-nonane, n-propanol, and their mixture on silver particles of three different sizes, the authors were able to estimate the line tensions and the microscopic contact angles for the above mentioned systems. To do this they applied generalized Young's equation for the line tension and calculated the interfacial tensions using Li and Neumann's equation [Adv. Colloid Interface Sci. 39, 299 (1992)]. It has been found that, for both unary and binary systems, the line tension is negative and the resulting microscopic contact angle derived from experimental nucleation data is most of the time larger than the macroscopic one. This is in contrast to earlier studies where the influence of line tension has not been accounted for. The values of the three phase contact line tension obtained in this way are of the same order of magnitude as the estimations for other systems reported in literature. The line tension effect also decreases considerably the nucleation barrier.     

An investigation of the stable orientations of orthorhombic particles in a thin film and their effect on its critical failure pressure

The effects of shape and contact angle on the behaviour of orthorhombic particles at an interface and in thin films were investigated using Surface Evolver. It is shown that the energetically stable orientations of the particle change with its aspect ratio. Long, wide, flat particles with low contact angles are more stable in flat orientations, i.e. with two faces parallel to the flat film surface. More cubic particles with higher contact angles are more stable in twisted orientations, where the opposite sides of the film can be drawn together at the sharp edges of the particle. The combination of contact angle and orientation has been found to have a large effect on the capillary pressure required to rupture the film. A film containing a particle in a flat orientation will rupture at a capillary pressure up to three times greater than one containing an identical particle in a twisted orientation. Wider, flatter particles with low contact angles stabilise thin liquid films to a greater extent than cubic particles with high contact angles.     

含氟丙烯酸酯聚合物乳胶膜表面性质

采用XPS和界面张力仪分别测定了含氟丙烯酸酯聚合物乳胶膜表面的组成及水在其表面的动态接触角, 并用状态逼近方程模型计算了含氟聚合物乳胶膜的表面张力, 考察了温度对乳胶膜润湿性的影响. 结果表明, 含氟聚合物乳胶膜表层较深处的F 1s信号强度比近表面要弱, 乳胶膜表面张力随表面氟原子浓度增加在一定程度上呈现线性下降；含氟侧链(Rf)较长(碳原子数n＞6)的含氟聚合物, 其表面张力随Rf单元含量增加而下降的趋势显著高于Rf较短(n≤6)的含氟聚合物, 而水在含氟聚合物乳胶膜表面上的后退接触角θr随n增大出现急剧上升, n≥10 时, θr值几乎恒定不再随n增大而改变. 此外, 参与共聚的非氟丙烯酸酯酯基碳链较短时, 水在共聚物乳胶膜表面的θr随氟单元含量增加而增加的趋势更显著；温度超过40 ℃后, 水对聚合物乳胶膜的润湿性随温度上升略有改善.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

Constitutive modeling of contact angle hysteresis

We introduce a phase field model of wetting of surfaces by sessile drops. The theory uses a two-dimensional non-conserved phase field variable to parametrize the Gibbs free energy of the three-dimensional system. Contact line tension and contact angle hysteresis arise from the gradient term in the free energy and the kinetic coefficient respectively. A significant advantage of this approach is in the constitutive specification of hysteresis. The advancing and receding angles of a surface, the liquid-vapor interfacial energy and three-phase line tension are the only required constitutive inputs to the model. We first simulate hysteresis on a smooth chemically homogeneous surface using this theory. Next we show that it is possible to study heterogeneous surfaces whose component surfaces are themselves hysteretic. We use this theory to examine the wetting of a surface containing a circular heterogeneous island. The contact angle for this case is found to be determined solely by the material properties at the contact line in accord with recent experimental data.     

Wetting on the microscale: shape of a liquid drop on a microstructured surface at different length scales

Describing wetting of a liquid on a rough or structured surface is a challenge because of the wide range of involved length scales. Nano- and micrometer-sized textures cause pinning of the contact line, reflected in a hysteresis of the contact angle. To investigate contact angles at different length scales, we imaged water drops on arrays of 5 μm high poly(dimethylsiloxane) micropillars. The drops were imaged by laser scanning confocal microscopy (LSCM), which allowed us to quantitatively analyze the local and large-scale drop profile simultaneously. Deviations of the shape of drops from a sphere decay at two different length scales. Close to the pillars, the amplitude of deviations decays exponentially within 1-2 μm. The drop profile approached a sphere at a length scale 1 order of magnitude larger than the pillars' height. The height and position dependence of the contact angles can be understood from the interplay of pinning of the contact line, the principal curvatures set by the topography of the substrate, and the minimization of the air-water interfaces.     

颗粒乳化剂的研究及应用

近年来,颗粒乳化剂因其在食品、采油、化妆品、医药、催化以及功能纳米材料制备等领域具有潜在应用前景而备受关注。本文综述了近来颗粒乳化剂的研究进展,归纳了颗粒乳化剂的种类,包括:无机纳米粒子、表面改性或杂化的无机粒子、有机纳米粒子以及特殊的颗粒乳化剂Janus粒子;并对颗粒乳化剂能够在油水界面稳定吸附的热力学机理和动力学行为进行了阐述,颗粒乳化剂在油水界面接触角以及粒径大小是其在界面稳定吸附的关键参数,而颗粒在油水界面的排布方式则主要受粒子之间相互作用的影响。重点介绍了颗粒乳化剂的热点应用,包括:(1)利用颗粒乳化剂制备Pickering乳液,以及通过对颗粒乳化剂的功能化,使得Pickering乳液具备环境响应性(即pH、盐浓度、温度、紫外光、磁场敏感响应性);(2)以颗粒乳化剂为构筑基元、以Pickering乳液为模板制备Janus颗粒、Colloidosome、具有多级结构的粒子或膜,以及多孔结构材料;(3) Janus粒子在催化领域的应用。     

Wetting properties of passivated metal nanocrystals at liquid-vapor interfaces: a computer simulation study

Molecular dynamics simulations have been employed to determine the contact angles of alkylthiol passivated gold nanocrystals adsorbed at the air-water interface. Simulations were performed using butane-, dodecane-, and octadecanethiol passivated nanoparticles. We demonstrate how the length of the surfactant chain can profoundly influence the wetting behavior of these nanoparticles. All particles were found to be stable at the air-water interface, possessing large, well-defined contact angles. We find that the shape of the dodecane- and octadecanethiol particles is strongly perturbed by the interface. We also present an analysis of the orientational ordering of water molecules at the dodecane-water interface and around butane- and dodecanethiol passivated nanoparticles. The orientational ordering translates into an electrostatic field around the nanoparticles, the magnitude of which corresponds with that of the water liquid-vapor interface.     

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.