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.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

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.     

Enhanced hydrophobicity of rough polymer surfaces

Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel's equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.     

Superhydrophobicity on two-tier rough surfaces fabricated by controlled growth of aligned carbon nanotube arrays coated with fluorocarbon

Considerable effort has been expended on theoretical studies of superhydrophobic surfaces with two-tier (micro and nano) roughness, but experimental studies are few due to the difficulties in fabricating such surfaces in a controllable way. The objective of this work is to experimentally study the wetting and hydrophobicity of water droplets on two-tier rough surfaces for comparison with theoretical analyses. To compare wetting on micropatterned silicon surfaces with wetting on nanoscale roughness surfaces, two model systems are fabricated: carbon nanotube arrays on silicon wafers and carbon nanotube arrays on carbon nanotube films. All surfaces are coated with 20 nm thick fluorocarbon films to obtain low surface energies. The results show that the microstructural characteristics must be optimized to achieve stable superhydrophobicity on microscale rough surfaces. However, the presence of nanoscale roughness allows a much broader range of surface design criteria, decreases the contact angle hysteresis to less than 1 degrees , and establishes stable and robust superhydrophobicity, although nanoscale roughness could not increase the apparent contact angle significantly if the microscale roughness dominates.     

以砂纸为模板制作聚合物超疏水表面

报道了一种聚合物材料超疏水表面的简便制备方法. 以不同型号的金相砂纸为模板, 通过浇注成型或热压成型技术, 在聚合物表面形成不同粗糙度的结构. 接触角实验结果证明, 聚合物表面与水的接触角随着所用砂纸模板粗糙度的增加而加大, 其中粒度号为W7和W5砂纸制作的表面与水的接触角可超过150°, 显示出超疏水性质. 多种聚合物使用砂纸为模均可制备不同粗糙度及超疏水的表面, 本征接触角对复制表面浸润性的影响从Wenzel态到Cassie态而变小. 扫描电镜结果表明, 不规则形状的砂纸磨料颗粒构成了超疏水所需要的微纳米结构的模板.     

Anisotropy in the wetting of rough surfaces

Surface roughness amplifies the water-repellency of hydrophobic materials. If the roughness geometry is, on average, isotropic then the shape of a sessile drop is almost spherical and the apparent contact angle of the drop on the rough surface is nearly uniform along the contact line. If the roughness geometry is not isotropic, e.g., parallel grooves, then the apparent contact angle is no longer uniform along the contact line. The apparent contact angles observed perpendicular and parallel to the direction of the grooves are different. A better understanding of this problem is critical in designing rough superhydrophobic surfaces. The primary objective of this work is to determine the mechanism of anisotropic wetting and to propose a methodology to quantify the apparent contact angles and the drop shape. We report a theoretical and an experimental study of wetting of surfaces with parallel groove geometry.     

Roughness assessment and wetting behavior of fluorocarbon surfaces

The wetting behavior of fluorocarbon materials has been studied with the aim of assessing the influence of the surface chemical composition and surface roughness on the water advancing and receding contact angles. Diamond like carbon and two fluorocarbon materials with different fluorine content have been prepared by plasma enhanced chemical vapor deposition and characterized by X-ray photoemission, Raman and FT-IR spectroscopies. Very rough surfaces have been obtained by deposition of thin films of these materials on polymer substrates previously subjected to plasma etching to increase their roughness. A direct correlation has been found between roughness and water contact angles while a superhydrophobic behavior (i.e., water contact angles higher than 150° and relatively low adhesion energy) was found for the films with the highest fluorine content deposited on very rough substrates. A critical evaluation of the methods currently used to assess the roughness of these surfaces by atomic force microscopy (AFM) has evidenced that calculated RMS roughness values and actual surface areas are quite dependent on both the scale of observation and image resolution. A critical discussion is carried out about the application of the Wenzel model to account for the wetting behavior of this type of surfaces.     

On the Problem of the Relationship between the Contact Angle and Surface Roughness Coefficient: Quartz Wettability with Melted Germanium

Equilibrium contact angles of melted geranium have been measured at fused quartz surfaces. The surfaces were preliminarily grinded, polished, and, in some cases, etched. Then, the roughness coefficients are determined for the relief profile and the surface itself by optical interferometry using a NanoMap 1000 WLI profilometer. The contact angle has been found to vary in a range of 147°–164° depending on the method of surface pretreatment. The measured values of the contact angles agree with the data of other researchers. At the same time, the analysis of the obtained data has led to the conclusion that Wenzel’s equation, which relates the contact angles at smooth and rough surfaces, is not valid for germanium droplets on quartz surface.     

Beyond the lotus effect: roughness influences on wetting over a wide surface-energy range

To enhance our understanding of liquids in contact with rough surfaces, a systematic study has been carried out in which water contact angle measurements were performed on a wide variety of rough surfaces with precisely controlled surface chemistry. Surface morphologies consisted of sandblasted glass slides as well as replicas of acid-etched, sandblasted titanium, lotus leaves, and photolithographically manufactured golf-tee shaped micropillars (GTMs). The GTMs display an extraordinarily stable, Cassie-type hydrophobicity, even in the presence of hydrophilic surface chemistry. Due to pinning effects, contact angles on hydrophilic rough surfaces are shifted to more hydrophobic values, unless roughness or surface energy are such that capillary forces become significant, leading to complete wetting. The observed hydrophobicity is thus not consistent with the well-known Wenzel equation. We have shown that the pinning strength of a surface is independent of the surface chemistry, provided that neither capillary forces nor air enclosure are involved. In addition, pinning strength can be described by the axis intercept of the cosine-cosine plot of contact angles for rough versus flat surfaces with the same surface chemistries.     

Wetting of real solid surfaces: new glance on well-known problems

The wetting of solid surfaces is treated. The Young and receding contact angles are experimentally unattainable values for the majority of solid surfaces. Actually, we always observe the apparent contact angle. This makes the characterization of wetting of real surfaces problematic. It is proposed in this paper to characterize wetting of real surfaces with the advancing contact angle and the minimum work of adhesion calculated according to the Dupre equation. The advancing contact angle, which depends slightly on the experimental technique used for its measurement, corresponds to the maximal solid/liquid surface tension and correspondingly to the minimal work of adhesion, calculated according to the Dupre equation.     

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.     

Conversion of a metastable superhydrophobic surface to an ultraphobic surface

Superhydrophobic surfaces in Wenzel and metastable wetting state were prepared and the conversion of such surfaces to ultraphobic surfaces was reported by the application of a fine-scale roughness. Silicon nitride substrates with hexagonally arranged pillars were prepared by micromachining. The two-scale roughness was achieved by coating these substrates with 60 nm silica nanoparticles. The surface was made hydrophobic by silanization with octadecytrichlorosilane (OTS). Wettability studies of the silicon nitride flat surface, silicon nitride pillars, and the surfaces with two-scale roughness showed that a two-scale roughness can effectively improve the hydrophobicity of surfaces with a higher apparent contact angle and reduced contact angle hysteresis when the original rough surface was in a metastable or Wenzel state. This study shows the pathway of converting a metastable hydrophobic surface to an ultraphobic surface by the introduction of a fine-scale roughness, which adds to the literature a new aspect of fine-scale roughness effect.     

Contact-angle hysteresis on super-hydrophobic surfaces

The relationship between perturbations to contact angles on a rough or textured surface and the super-hydrophobic enhancement of the equilibrium contact angle is discussed theoretically. Two models are considered. In the first (Wenzel) case, the super-hydrophobic surface has a very high contact angle and the droplet completely contacts the surface upon which it rests. In the second (Cassie-Baxter) case, the super-hydrophobic surface has a very high contact angle, but the droplet bridges across surface protrusions. The theoretical treatment emphasizes the concept of contact-angle amplification or attenuation and distinguishes between the increases in contact angles due to roughening or texturing surfaces and perturbations to the resulting contact angles. The theory is applied to predicting contact-angle hysteresis on rough surfaces from the hysteresis observable on smooth surfaces and is therefore relevant to predicting roll-off angles for droplets on tilted surfaces. The theory quantitatively predicts a "sticky" surface for Wenzel-type surfaces and a "slippy" surface for Cassie-Baxter-type surfaces.     

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.     

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.     

Wetting and wetting transitions on copper-based super-hydrophobic surfaces

Rough and patterned copper surfaces were produced using etching and, separately, using electrodeposition. In both of these approaches the roughness can be varied in a controlled manner and, when hydrophobized, these surfaces show contact angles that increase with increasing roughness to above 160 degrees . We show transitions from a Wenzel mode, whereby the liquid follows the contours of the copper surface, to a Cassie-Baxter mode, whereby the liquid bridges between features on the surface. Measured contact angles on etched samples could be modeled quantitatively to within a few degrees by the Wenzel and Cassie-Baxter equations. The contact angle hysteresis on these surfaces initially increased and then decreased as the contact angle increased. The maximum occurred at a surface area where the equilibrium contact angle would suggest that a substantial proportion of the surface area was bridged.     

微结构疏水表面上液滴的表观接触角

虽然微结构疏水表面上Cassie-Baxter状态液滴的表观接触角已有理论预测公式,但实验研究发现,由于微结构疏水表面上的瑕疵,以及液滴受到的各种轻微扰动等原因,很容易造成Cassie-Baxter状态液滴局部区域出现Wenzel状态的情况(即混合状态),而有关混合状态液滴表观接触角的研究还比较少.本文通过对比相同微结构疏水表面上Cassie-Baxter状态和混合状态液滴表观接触角的大小,发现将Cassie-Baxter预测公式中的固液接触面积分数F换成最外缘三相接触线处的局部固液接触面积分数F′,则能同时较好地预测上述两种情况下液滴的表观接触角;通过进一步的研究发现,表观接触角的大小仅与最外缘三相接触线处的固液接触状态有关,而与其他处的固液接触状态无关.该结果对于进一步认识微结构疏水表面上液滴的表观接触角以及润湿性质具有重要意义.     

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.