Model and experimental studies for contact angles of surfactant solutions on rough and smooth hydrophobic surfaces

Despite the practical need, no models exist to predict contact angles or wetting mode of surfactant solutions on rough hydrophobic or superhydrophobic surfaces. Using Gibbs' adsorption equation and a literature isotherm, a new model is constructed based on the Wenzel and Cassie equations. Experimental data for aqueous solutions of sodium dodecyl sulfate (SDS) contact angles on smooth Teflon surfaces are fit to estimate values for the adsorption coefficients in the model. Using these coefficients, model predictions for contact angles as a function of topological f (Cassie) and r (Wenzel) factors and SDS concentration are made for different intrinsic contact angles. The model is also used to design/tune surface responses. It is found that: (1) predictions compare favorably to data for SDS solutions on five superhydrophobic surfaces. Further, the model predictions can determine which wetting mode (Wenzel or Cassie) occurred in each experiment. The unpenetrated or partially penetrated Cassie mode was the most common, suggesting that surfactants inhibit the penetration of liquids into rough hydrophobic surfaces. (2) The Wenzel roughness factor, r, amplifies the effect of surfactant adsorption, leading to larger changes in contact angles and promoting total wetting. (3) The Cassie solid area fraction, f, attenuates the lowering of contact angles on rough surfaces. (4) The amplification/attenuation is understood to be due to increased/decreased solid-liquid contact-area.     

Patterned nonadhesive surfaces: superhydrophobicity and wetting regime transitions

Nonadhesive and water-repellent surfaces are required for many tribological applications. We study mechanisms of wetting of patterned superhydrophobic Si surfaces, including the transition between various wetting regimes during microdroplet evaporation in environmental scanning electron microscopy (ESEM) and for contact angle and contact angle hysteresis measurements. Wetting involves interactions at different scale levels: macroscale (water droplet size), microscale (surface texture size), and nanoscale (molecular size). We propose a generalized formulation of the Wenzel and Cassie equations that is consistent with the broad range of experimental data. We show that the contact angle hysteresis involves two different mechanisms and how the transition from the metastable partially wetted (Cassie) state to the homogeneously wetted (Wenzel) state depends upon droplet size and surface pattern parameters.     

Condensation-induced wetting state and contact angle hysteresis on superhydrophobic lotus leaves

In this paper, we demonstrate how condensed moisture droplets wet classical superhydrophobic lotus leaf surfaces and analyze the mechanism that causes the increase of contact angle hysteresis. Superhydrophobic lotus leaves in nature show amazing self-cleaning property with high water contact angle (>150°) and low contact angle hysteresis (usually <10°), causing droplets to roll off at low inclination angles, in accordance with classical Cassie–Baxter wetting state. However, when superhydrophobic lotus leaves are wetted with condensation, the condensed water droplets are sticky and exhibit higher contact angle hysteresis (40–50°). Compared with a fully wetted sessile droplet (classical Wenzel state) on the lotus leaves, the condensed water droplet still has relatively large contact angle (>145°), suggesting that the wetting state deviates from a fully wetted Wenzel state. When the condensed water droplets are subjected to evaporation at room conditions, a thin water film is observed bridging over the micropillar structures of the lotus leaves. This causes the dew to stick to the surface. This result suggests that the condensed moisture does not uniformly wet the superhydrophobic lotus leaf surfaces. Instead, there occurs a mixed wetting state, between classical Cassie–Baxter and Wenzel states that causes a distinct increase of contact angle hysteresis. It is also observed that the mixed Cassie–Baxter/Wenzel state can be restored to the original Cassie–Baxter state by applying ultrasonic vibration which supplies energy to overcome the energy barrier for the wetting transition. In contrast, when the surface is fully wetted (classical Wenzel state), such restoration is not observed with ultrasonic vibration. The results reveal that although the superhydrophobic lotus leaves are susceptible to being wetted by condensing moisture, the configured wetting state is intermediate between the classical Cassie–Baxter and Wenzel states.     

Pressure induced transition between superhydrophobic states: configuration diagrams and effect of surface feature size

The stability of wetting states, namely the Cassie state (partial wetting) and the Wenzel state (complete wetting) of surfaces with protrusions, is determined by comparing the total free energy of a liquid drop in terms of their apparent contact angles for different protrusion features. It is found that when the area fraction of the topographical features and the intrinsic contact angle for a flat surface are large, the Cassie state is favored, but it can be either the metastable or stable state. It is shown that the transition from the Cassie state to the Wenzel state requires the application of a pressure to the meniscus between the surface protrusions. The critical transition pressure increases not only with increasing area fraction and intrinsic contact angle, but also with decreasing protrusion size. During the transition, a high-pressure gas can be trapped around the protrusions that can cause the Cassie state to be recovered after the release of the applied pressure. The analysis shows that a droplet can 'hang' upside-down when the protrusion size is very small; namely, the protrusions can pin the meniscus. These results are discussed relative to the advancing and receding contact angle.     

Contact angle hysteresis on regular pillar-like hydrophobic surfaces

A series of pillar-like patterned silicon wafers with different pillar sizes and spacing are fabricated by photolithography and further modified by a self-assembled fluorosilanated monolayer. The dynamic contact angles of water on these surfaces are carefully measured and found to be consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Wenzel state, its contact angle hysteresis increases along with an increase in the surface roughness. While the surface roughness is further raised beyond its transition roughness (from the Wenzel state to the Cassie state), the contact angle hysteresis (or receding contact angle) discontinuously drops (or jumps) to a lower (or higher) value. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction and has nothing to do with the surface roughness. Even for a superhydrophobic surface, the contact angle hysteresis may still exhibit a value as high as 41 degrees for the solid fraction of 0.563.     

Control over wettability of polyethylene glycol surfaces using capillary lithography

We demonstrate that wettability of poly(ethylene glycol) (PEG) surfaces can be controlled using nanostructures with various geometrical features. Capillary lithography was used to fabricate PEG nanostructures using a new ultraviolet (UV) curable mold consisting of functionalized polyurethane with acrylate group (MINS101m, Minuta Tech.). Two distinct wetting states were observed depending of the height of nanostructures. At relatively lower heights (< 300 nm for 150 nm pillars with 500 nm spacing), the initial contact angle of water was less than 80 degrees and the water droplet easily invaded into the surface grooves, leading to a reduced contact angle at equilibrium (Wenzel state). At relatively higher heights (> 400 nm for 150 nm pillars with 500 nm spacing), on the other hand, the nanostructured PEG surface showed hydrophobic nature and no significant change in contact angle was observed with time (Cassie state). The presence of two wetting states was also confirmed by dynamic wetting properties and contact-angle hysteresis. The wetting transition from hydrophilic (bare PEG surface) to hydrophobic (PEG nanostructures) was described by the Cassie-Baxter equation assuming that enhanced hydrophobicity is due to the heterogeneous wetting mediated by an air pocket on the surface. The measured contact angles in the Cassie state were increased with increasing air fraction, in agreement with the theoretical prediction.     

A stable intermediate wetting state after a water drop contacts the bottom of a microchannel or is placed on a single corner

It is considered that, after a water drop contacts the base of a roughness groove, water should immediately fill this roughness groove. Subsequently, Cassie-Baxter wetting state is transited to that of Wenzel. Accordingly, one of the criteria used to judge the transition from Cassie-Baxter to Wenzel states is whether a water drop has contact with the base of a roughness groove. In this work, through theoretical and experimental investigations, we show that this transition criterion does not always hold true in the case of microchannels. We first theoretically prove that, when an angle criterion is satisfied, there may exist an intermediate wetting state inside a microchannel after a water drop contacts the bottom of the microchannel. In this wetting state, water does not completely fill the microchannel, and air pockets still exist in its bottom corners. Also, the wetting state is stable in the sense that its energy state is lower than that of the Wenzel model. According to the angle criterion, such intermediate states may exist, for example, in microchannels with vertical sidewalls, when contact angles on the inner surfaces of these microchannels are larger than 135°. In addition to microchannels, the aforementioned intermediate state may also exist on a single corner (which is formed by a horizontal plate and an inclined plate), when the angle criterion is met. After theoretical modeling, we then conduct four types of tests on single corners and microchannels to validate the angle criterion. In these tests, once the angle criterion is met, stable intermediate states are observed on the corresponding samples. In addition, it is found from the two types of tests conducted on microchannels that, once Laplace pressure inside a water drop is gradually reduced, such an intermediate wetting state may be transited back to the original Cassie-Baxter state. On the other hand, the Wenzel state may not have such a reversal transition unless an additional force is applied to overcome energy barrier between Wenzel and Cassie-Baxter states.     

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.     

Direct Insight into the Three‐Dimensional Internal Morphology of Solid–Liquid–Vapor Interfaces at Microscale

Solid–liquid–vapor interfaces dominated by the three‐phase contact line, usually performing as the active center in reactions, are important in biological and industrial processes. In this contribution, we provide direct three‐dimensional (3D) experimental evidence for the inside morphology of interfaces with either Cassie or Wenzel states at micron level using X‐ray micro‐computed tomography, which allows us to accurately “see inside” the morphological structures and quantitatively visualize their internal 3D fine structures and phases in intact samples. Furthermore, the in‐depth measurements revealed that the liquid randomly and partly located on the top of protrusions on the natural and artificial superhydrophobic surfaces in Cassie regime, resulting from thermodynamically optimal minimization of the surface energy. These new findings are useful for the optimization of classical wetting theories and models, which should promote the surface scientific and technological developments.     

Superhydrophobic surfaces and emerging applications: Non-adhesion,energy, green engineering

This paper provides a review of superhydrophobicity and related phenomena (superoleophobicity, omniphobicity, self-cleaning) induced by surface micro- and nanostructuring. The classical approaches to superhydrophobicity using the Young, Wenzel, and Cassie–Baxter models for the contact angle (CA) are presented. After that, the issues that are beyond the Wenzel and Cassie–Baxter theories are discussed, such as multiscale effects, 1D vs. 2D interactions, the effects of contact line, size of roughness details, curvature, and CA hysteresis dependence on roughness. New potential applications of superhydrophobicity are reviewed, such as new ways of energy transition, antifouling, and environment-friendly manufacturing.     

Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles

Superhydrophobicity is obtained on photolithographically structured silicon surfaces consisting of flat-top pillars after a perfluorosilanization treatment. Systematic static contact angle measurements were carried out on these surfaces as a function of pillar parameters that geometrically determine the surface roughness, including pillar height, diameter, top perimeter, overall filling factor, and disposition. In line with thermodynamics models, two regimes of static contact angles are observed varying each parameter independently: the "Cassie" regime, in which the water drop sits suspended on top of the pillars (referred to as composite), corresponding to experimental contact angles greater than 140-150 degrees, and the "Wenzel" regime, in which water completely wets the asperities (referred to as wetted), corresponding to lower experimental contact angles. A transition between the Cassie and Wenzel regimes corresponds to a set of well-defined parameters. By smoothly depositing water drops on the surfaces, this transition is observed for surface parameter values far from the calculated ones for the thermodynamic transition, therefore offering evidence for the existence of metastable composite states. For all studied parameters, the position of the experimental transition correlates well with a rough estimation of the energy barrier to be overcome from a composite metastable state in order to reach the thermodynamically favored Wenzel state. This energy barrier is estimated as the surface energy variation between the Cassie state and the hypothetical composite state with complete filling of the surface asperities by water, keeping the contact angle constant.     

Condensation and wetting transitions on microstructured ultra-hydrophobic surfaces

On rough surfaces, two distinct wetting modes can appear. These two states are usually described by the theories of Cassie (drops suspended on top of roughness features) and Wenzel (drops impaled on roughness features). Whereas the wetting transition from the Cassie to the Wenzel state has been relatively well studied both experimentally and theoretically, the question of whether metastable Wenzel drops exist and how they transition to the Cassie state has remained open. In this work, we study the wetting behavior of microstructured post surfaces coated with a hydrophobic fluoropolymer. Through condensation, the formation of metastable Wenzel droplets is induced. We show that under certain conditions drops can transition from the Wenzel to the Cassie state.     

Fabrication of hydrophobic surfaces by coupling of Langmuir-Blodgett deposition and a self-assembled monolayer

A novel method coupling the Langmuir-Blodgett (LB) deposition of silica particles and the formation of a self-assembled monolayer (SAM) of alkylsilane is proposed for fabricating hydrophobic surfaces. The LB deposition and the SAM are supposed to confer the substrate surface roughness and low surface energy, respectively. By controlling the hydrophobic-hydrophilic balance of the silica particle surface through the adsorption of surfactant molecules, deposition of monolayers consisting of hexagonally close-packed arrays of particles on a glass substrate can then be successfully conducted in a Langmuir trough. LB particulate films with a particle layer number up to 5 were thereby prepared. A sintered and hydrophobically finished particulate film with roughness factor of 1.9 was finally fabricated by sintering and surface silanization. Effects of particle size and particle layer number on the wetting behavior of the particulate films were systematically studied by measuring static and dynamic water contact angles. The experimental results revealed that a static contact angle of about 130 degrees resulted from the particulate films regardless of the particle size and particle layer number. This is consistent with the predictions of both the Wenzel model and the Cassie and Baxter model in that roughness of a hydrophobic surface can increase its hydrophobicity and a switching of the dominant mode from Wenzel's to Cassie and Baxter's. In general, an advancing contact angle of about 150 degrees , a receding contact angle of about 110 degrees , and a contact angle hysteresis of about 40 degrees were exhibited by the particulate films fabricated.     

On the validity of the Cassie equation via a mean-field free-energy lattice Boltzmann approach

We studied wetting phenomena on heterogeneous surfaces by a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 69 (2004) 32,602]. Our results suggest that the Cassie equation in macroscopic contact angle measurements is in general not valid. It was found that the Cassie equation is valid only when the patch size is on the same order of the liquid-vapor interfacial thickness. We also demonstrated that contact angle manifests itself from local surface properties near the contact point and does not result from the specific solid-liquid interactions across the contact area.     

Effect of nanobubbles on friction forces between hydrophobic surfaces in water

Micro- and nanoscale combined hierarchical polymer structures were fabricated by UV-assisted capillary force lithography. The method is based on the sequential application of engraved polymer molds with a UV-curable resin of polyurethane acrylate (PUA) followed by surface treatment with a trichloro(1H,1H,2H,2H-perfluorooctyl) silane in vapor phase. Two distinct wetting states were observed on these dual-roughness structures. One is “Cassie–Wenzel state” where a water droplet forms heterogeneous contact with microstructures and homogeneous contact with nanostructures. The other is “Cassie–Cassie state” where a droplet makes heterogeneous contact both with micro- and nanostructures. A simple thermodynamic model was developed to explain static contact angle, hysteresis, and wetting transition on dual-roughness structures.     

Wetting on nanoporous alumina surface: transition between Wenzel and Cassie states controlled by surface structure

This paper reports a systematic study on the relationship between surface structure and wetting state of ordered nanoporous alumina surface. The wettability of the porous alumina is dramatically changed from hydrophilicity to hydrophobicity by increasing the hole diameter, while maintaining the hole interval and depth. This phenomenon is attributed to the gradual transition between Wenzel and Cassie states which was proved experimentally by comparing the wetting behavior on these porous alumina surfaces. Furthermore, the relationship between surface wettability and hole depth at a fixed hole interval and diameter was investigated. For those porous alumina with relatively larger holes in diameter, transition between Wenzel and Cassie states was also achieved with increasing hole depth. A capillary-pressure balance model was proposed to elucidate the unique structure-induced transition, and the criteria for the design and construction of a Cassie wetting surface was discussed. These structure-induced transitions between Wenzel and Cassie states could provide further insight into the wetting mechanism of roughness-induced wettability and practical guides for the design of variable surfaces with controllable wettability.     

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

图案化基底上液滴的挥发行为

采用液滴形状分析仪, 在线跟踪了液滴在图案化基底上的挥发过程. 结果表明, 与平滑基底结果相比, 图案化基底上的挥发过程明显不同. 首先, 接触角减小; 另外, 由于发生了Cassie态到Wenzel态转变, 所得接触直径在减小过程中产生了一个突然变大的阶段. 在该挥发过程中, 突起部分的面积分数扮演了十分重要的角色.     

Fabrication of superhydrophobic surfaces from microstructured ZnO-based surfaces via a wet-chemical route

The fabrication of a superhydrophobic surface is demonstrated via a wet chemical route, and this method offers advantages of being cleanroom free, cost efficiency, and wide applicability. The preferable growth of ZnO crystalline forms a microstructured surface, and a variety of alkanoic acids were adopted to tune the surface wettability. Although all surfaces show an advancing contact angle greater than 150 degrees , they substantially differ in the wetting mechanisms. It is found that only when the length of alkanoic acid is greater than 16, the microstructured surface shows a stable superhydrophobicity, in which the Cassie state dominates. While for those moderate-length alkanoic acids (C8-C14), their corresponding surfaces have a tendency to fall into the Wenzel state and display a great contact angle hysteresis.