Cassie-Baxter Equation Research Articles

마이크로 기둥 구조가 있는 친수성/소수성 표면에서의 겉보기 접촉 각에 대한 연구

In this study, the apparent contact angle on the hydrophilic/hydrophobic surfaces with micropillars was studied. The previous researches showed that the Wenzel equation and the Cassie-Baxter equation were thermodynamically derived for the rough hydrophilic/hydrophobic surfaces and generally referenced on the field of wetting phenomena. For the verification of both equations, the apparent contact angle on the hydrophilic/hydrophobic surfaces with micro-pillars was measured. In the comparison between the measured and estimated apparent contact angles with the equations, the differences between the apparent contact angles were analyzed. Conclusively, the available range and limitation of theoretical equations were investigated and further researches about the apparent contact angle on the rough surfaces were proposed.

The effect of drop size on contact angle measurements of superhydrophobic surfaces

In this study, the effect of drop volume on contact angle (CA) values and also on the applicability of the Cassie–Baxter equation is experimentally investigated. To do this, dimethyldichlorosilane (DMDCS) coated different sized square pillar surfaces with varying fCBs(geo) values were used. Varying water drop volumes between 0.5 μl and 19 μl were used to measure CA's on square pillar surfaces with different pattern sizes changing from 8 μm to 40 μm. It was found that experimental CA values remained constant for each drop volume, indicating that increase or decrease in drop volume had no significant effect on experimentally measured CA values of square pillar surfaces with varying pattern sizes and fCBs(geo) values. When the relationship between the applicability of the Cassie–Baxter equation and the drop volume was investigated, it was also found that variation in volume of the drop did not cause a significant change in deviations between the theory and the experiments. ΔθCB values remained almost constant for all samples at varying drop volumes.

Modification of the wettability of polymer surfaces using nanoparticles

The effects of nanoparticles, embedded into the matrices of polymer films, on the wettabilities of the surfaces of the composite films are investigated following a two-fold procedure. First, five particles such as silica (of two sizes), tin oxide, alumina and zinc oxide ranged from 7 to 100nm are mixed with a poly(methyl siloxane). Second, silica nanoparticles (7nm) are embedded in five different polymers such as poly(methyl methacrylate), polystyrene and three poly (alkyl siloxane) products. Nanocomposite films are produced by adding nanoparticles in the polymer solutions which are then sprayed on silicon substrates.In the first study, which includes the use of different nanoparticles, the contact angle hysteresis is monitored as a function of particle concentration. It is shown that similar water repellency that corresponds to hysteresis <5° is achieved using any of the five tested particles when these are mixed with the siloxane at elevated concentrations. However, the wettability of film surfaces prepared using dispersions of low particle concentration, is highly affected by the particle size and concentration: (i) water repellency of the modified polymer surfaces is enhanced when nanoparticles of small sizes are used i.e. films prepared using particles of small sizes correspond to lower hystereses compared to films produced using bigger particles. (ii) As the particle concentration increases, we first notice an increase in hysteresis, which then decreases. This result is explained with respect to the surface morphologies of the films which are revealed using Scanning Electron Microscopy (SEM).In the second study, which includes the use of different polymers, it is shown that superhydrophobicity can be achieved using any of the previously mentioned organic materials. According to SEM images, similar continuous rough structures are formed on the surfaces of the films, prepared using different polymers and (the same) silica nanoparticles. This is supported by the Cassie-Baxter equation which suggests that comparable surface porosity factors correspond to the different composite films.

Influence of topography on plasma treated titanium surface wettability

With the aim of studying the topographic influence on wettability of plasma-treated surfaces, we used eighteen commercially pure titanium (CP Titanium) disks (grade II), 10mm in diameter and 1mm thick, and in atmospheres of Argon (Ar), Hydrogen H2 and Ar–H2. These samples were submitted to plasma produced by hollow cathode discharge (HCD) for 20 and 60min at a voltage of 500V and pressure of 220Pa. After pre-treatment, the state of the sample surfaces was assessed for surface phases with grazing incidence X-ray diffraction (GIXRD), and XPS (X-ray photoelectron spectroscopy), evaluated by atomic force microscopy (AFM) and wettability, using the sessile drop test. It was found that all the conditions were effective in reducing oxide, resulting in different wettability values. Correlation between average roughness (Ra) parameters and the ratio between maximum peak height and average distance between the highest peak and lowest valley (Rp/Rz) and wettability for the different treatment conditions were analyzed. Given the results obtained, it was concluded that Ra and Rp/Rz are not appropriate for correlating with wettability and it is suggested that a new topographic parameter be adopted for the Cassie–Baxter equation. XPS analysis showed that reduction efficacy was greater for the Ar–H2 mixture, followed by Ar and H2.

Validity of the equations for the contact angle on real surfaces

The wetting property between liquid and solid is very important in many industries besides natural systems. The simplest method to determine the wetting property is just dropping a liquid drop on a solid surface and measuring a contact angle from the shape of the drop. Since the Young’s equation has been used as a basic equation to relate a contact angle and interfacial tensions over 200 years, it is important to understand a derivation and limits of the Young’s equation. We derived the Young’s equation following energy minimization with simple mathematics. By expanding the derivation, the modified forms of the Cassie-Baxter equation and the Wenzel equation were also derived. From analyses of the derivations, it was deduced that a contact angle on an ideal surface is only related to the infinitesimal region in the vicinity of contact line, not internal area surrounded by the contact line. Although the Cassie-Baxter model and the Wenzel model were not rigorously built, they have been widely used for a superhydrophobic surface, because the apparent forms are similar to those of rigorously derived models when the contact line can easily move on the surface.

Estimation of contact angle for hydrophobic silica nanoparticles in their hexagonally ordered layer

Wetting properties of bilayered nanostructured coatings were studied in this work. Coatings were prepared by stratifying a compact silica sol–gel (SG) film and a Langmuir–Blodgett (LB) layer of differently sized (84, 131 and 227 nm) Stöber silica particles onto glass substrates. Joint high temperature annealing of the layers increased the mechanical stability of the particulate film facilitating its further investigations.Regular structure of LB layers allowed us to carry out wetting model investigations. Close-packed arrangement of particles was reinforced by optical measurements. Transmittance spectra of LB films were taken and evaluated by a theoretical model. Resulting effective refractive index and film thickness values indicated a good agreement between the real and the supposed (hexagonally close packed, monodisperse spherical particles) layer structure. It was confirmed by field emission scanning electron microscopy (FESEM) images, too.Advancing and receding water contact angles (CA) on differently (with mono- and bifunctional chlorosilanes) hydrophobized SG and combined films were measured applying the sessile drop method. SG films showed approximately the same CA-s after different silylation processes without considerable contact angle hysteresis (CAH). In case of combined films ca. 30° higher advancing CA-s were measured at stronger silylation and only the milder silylation resulted in significant CAH. It was explained by the surface heterogeneity of constituent particles. Layers of differently sized particles showed the same wetting properties in all cases in agreement to the Cassie–Baxter equation which was used for the estimation of CA values for the individual silica particles (88–90° and 105–106° depending on the silylation conditions).

Hydrophobic diamond films

The peculiarities of wettability of diamond that was obtained in a nanostructured form as ultrananocrystalline diamond (UNCD) films by deposition from a gas phase are considered. Surface hydrogenation leads to hydrophobicity: advancing contact angle θ for UNCD films reaches 106 ± 1° (for diamond single crystals θ = 93°). Even higher values of θ equal to 124 ± 3° were detected for nanoporous samples of UNCD, in which a graphite-like component was removed by etching. High hydrophobicity is achieved owing to the specific surface morphology of the nanostructured diamond (anisotropic, with high content of nanopores) and chemical modification, which on the whole provides for very low values of free surface energy of the films. It was shown that laser-drilled microholes in polycrystalline diamond also can enhance the hydrophobicity. The wetting behavior of the nanostructured surfaces agrees well with the Cassie-Baxter equation for heterophase porous surfaces. The oxidation and hydrogenation of UNCD films allows controlling of θ in considerably wider ranges compared to single crystal diamond.

Theoretical progress in designs of stable superhydrophobic surfaces

Controlling the wettability of solid surfaces is an important issue that has aroused the increasing interest from both fundamental and practical perspective by tailoring surface morphology and surface chemical compositions. The underlying theories for interpreting wetting phenomena still mainly focus on the Young's equation, the Wenzel equation, and the Cassie-Baxter equation, despite the fact that the wetting phenomena have been studied over the past decades. While there are a lot of experimental studies on wettability of surface roughness, there is still a lack of a thorough analysis of the contributions of micro and nano-scale roughness to wettability behavior despite interesting features these surfaces have. In this article, the basic theories and their applicabilities are addressed in detail, and the mutual transition between Wenzel state and Cassie-Baxter state is described from different viewpoints in general, and from single-scale and dual-scale point of view in particular. The design concept of geometrical model with stable superhydrophobicity is also described, which is based on the typical theories about wettability. Finally, some promising breakthroughs in the theoretical progress are proposed.

Synthesis and Surface Properties of Hierarchical SiO2 Coating Layers by Forming Au Nanoparticles

Superhydrophobic <TEX>$SiO_2$</TEX> layers with a micro-nano hierarchical surface structure were prepared. <TEX>$SiO_2$</TEX> layers deposited via an electrospray method combined with a sol-gel chemical route were rough on the microscale. Au particles were decorated on the surface of the microscale-rough <TEX>$SiO_2$</TEX> layers by use of the photo-reduction process with different intensities (<TEX>$0.11-1.9mW/cm^2$</TEX>) and illumination times (60-240 sec) of ultraviolet light. With the aid of nanoscale Au nanoparticles, this consequently resulted in a micro-nano hierarchical surface structure. Subsequent fluorination treatment with a solution containing trichloro(1H,2H,2H,2H-perfluorooctyl)silane fluorinated the hierarchical <TEX>$SiO_2$</TEX> layers. The change in surface roughness factor was in good agreement with that observed for the water contact angle, where the surface roughness factor developed as a measure needed to evaluate the degree of surface roughness. The resulting <TEX>$SiO_2$</TEX> layers revealed excellent repellency toward various liquid droplets with different surface tensions ranging from 46 to 72.3 mN/m. Especially, the micro-nano hierarchical surface created at an illumination intensity of <TEX>$0.11mW/cm^2$</TEX> and illumination time of 60 sec showed the largest water contact angle of <TEX>$170^{\circ}$</TEX>. Based on the Cassie-Baxter and Young-Dupre equations, the surface fraction and work of adhesion for the micronano hierarchical <TEX>$SiO_2$</TEX> layers were evaluated. The work of adhesion was estimated to be less than <TEX>$3{\times}10^{-3}N/m$</TEX> for all the liquid droplets. This exceptionally small work of adhesion is likely to be responsible for the strong repellency of the liquids to the micro-nano hierarchical <TEX>$SiO_2$</TEX> layers.

Influence of long alkyl spacers in the elaboration of superoleophobic surfaces with short fluorinated chains

In order to produce extremely high oleophobic properties with a low fluorine content, long dodecyl spacers were introduced between a polymer and fluorinated chains in order to reduce the mobility of the fluorinated chains, especially short perfluorobutyl (F-butyl) chains. We report the synthesis and characterization of electrodeposited polymer surfaces obtained from original fluorinated 3,4-ethylenedioxypyrrole (EDOP) derivatives. Semi-fluorinated chains of three different lengths (F-octyl: PEDOPC12F8, F-hexyl: PEDOPC12F6 and F-butyl: PEDOPC12F4) were grafted to EDOP and separated with a n-dodecyl chain in order to reduce the mobility of F-butyl chains. For the first time, a surprisingly high contact angle of 138° was measured with hexadecane on PEDOPC12F4, although F-octyl tails are necessary to produce robust superoleophobic surfaces. By producing smooth surfaces, we successfully separate the influence of the intrinsic hydro- and oleophobicity and the surface structuration on the static contact angles of water and hexadecane. Here, the surface structuration increases the contact angle of hexadecane by 90° for PEDOPC12F4. The Cassie–Baxter equation predicts a porosity of 84.5% between the surface and a hexadecane droplet.

Wetting behaviour of hydrophilic and hydrophobic nanostructured porous anodic alumina

This paper investigates the effect of surface structure and chemistry on the wetting properties of nanostructured porous anodic alumina (PAA). Measurements of the equilibrium apparent contact angle (APCA) were first taken on as produced hydrophilic nanoporous alumina with a range of pore diameters from 10 to 170nm, yielding a range of contact angles from 10 to 100°. The PAAs were then coated with a fluorosilane to change the surface chemistry of the nanostructures. The same trend was observed as in the hydrophilic case, but the contact angles increased from 106 to 150° for pores sizes ranging from 10 to 100nm for the hydrophobic PAA. These results probe the limits of the current wetting models such as the Cassie-Baxter and Wenzel equations for nanostructured materials. A geometric model has been developed using the equation proposed by Marmur to explain the wetting properties of the bare- and silanized-PAA.

Development of superhydrophilic and superhydrophobic polyester fabric by growing Zinc Oxide nanorods

ZnO nanorods were grown on microfibers of Polyethylene terephthalate (PET) fabric by seeding method to develop hierarchical roughness structure. XRD and XPS analysis show the presence of crystalline ZnO and chemical Zn species at the fiber surface at each stage of the process. Five series of samples with different seed concentrations have been realized, and their surface morphology and topography were characterized by AFM and SEM. Increasing seed concentrations lead to samples with superhydrophilic properties. Not only the water contact angle at fabric surface tends to zero but also the water capillary diffusion inside fabric is faster. Nanostructuration affects the structure inside the fabric, and further experiments with decane liquid have been made to get a better understanding of this effect. To study the superhydrophobicity, nanorods treated samples were modified with octadecyltrimethoxysilane (ODS) by two method; solution deposition and vapor deposition. The superhydrophobicity was characterized by measuring the water contact angle and water sliding angle with 5μl water droplet. The samples modified with ODS by vapor deposition showed higher water contact angles and low water sliding angle than the ones modified with solution method. The lotus effect has been well correlated with the surface morphology of the nanorods structured fibers. The application of the Cassie–Baxter equation is discussed.

Superhydrophobic surfaces

AbstractSuperhydrophobicity – also known as water repellency – has recently attracted considerable attention because of its numerous potential applications. However, the fundamental concepts and equations describing the wettability of superhydrophobic surfaces have been known since the 1940s. These concepts are reviewed and discussed in the present feature article in light of the recent developments. Furthermore, the potential use of water-repellent siloxane-nanoparticle composites for surface protection and consolidation of stones and mortars used in outdoor objects of cultural heritage is investigated. Finally, it is shown that the wettability of the composite surfaces can be predicted by the Cassie-Baxter equation.

Advances in the theory of superhydrophobic surfaces

The underlying theories interpreting wetting phenomena are still mainly focused on the Young's equation, the Wenzel equation, and the Cassie–Baxter equation, despite the fact that wetting phenomena have been studied over the past decades. Based on these theories, people have understood that both surface chemical composition and its morphology can influence the contact angle of liquid droplets on solid surfaces. However, such equations are not sufficient to thoroughly explain the mechanisms of wetting phenomena, although they are still necessary. In this feature article, we review the theory, from the classical wetting models to the most recent theoretical advances, of superhydrophobic surfaces with regard to the wetting process, and some promising breakthroughs in the advance of the theory are proposed in the final section.

Wetting properties of gas diffusion layers: Application of the Cassie-Baxter and Wenzel equations.

Wetting properties of gas diffusion layers: Application of the Cassie-Baxter and Wenzel equations.

Fractal characteristics and wettability of Nano-Al 2O 3/Ni-Co composite coating prepared by electrodeposition

Nano-Al 2O 3/Ni-Co composite coatings were formed on gray cast iron surface by electrodeposition method. The composite coating has a more flat surface and compact microstructure than the pure Ni-Co coating. The fractal surface structure parameters were calculated by fractal theory and the average fractal dimension is 1.301 3. The contact angles were measured and the maximum value reaches 105°. The relationship between wettability and fractal structure was explained by Cassie–Baxter equation. The results indicate that wetting behavior varies with the fractal dimension. But the change of contact angels is not directly proportional to the fractal dimension.

Effect of pattern size and geometry on the use of Cassie–Baxter equation for superhydrophobic surfaces

Cassie–Baxter equation depending on the extent of liquid/solid interfacial contact area was generally used in the past to estimate water contact angles on superhydrophobic surfaces. However, there are objections refuting the contact area based equations and suggesting that the three-phase contact line determines the apparent contact angle. In this study, we tested the validity of Cassie–Baxter equation on superhydrophobic surfaces. 36 pattern samples made of square and 24 of cylindrical pillars were prepared by applying the DRIE technique on Si-wafers. Pillar side lengths and diameters were varied between 8 and 100 μm and the height of pillars was kept nearly constant between 30 and 34 μm. 18 square and 12 cylindrical patterns were coated by hydrophobic dimethyldichlorosilane vapor to obtain superhydrophobic surfaces. Recent method of Erbil and Cansoy was used to test the validity of Cassie–Baxter equation to estimate the water contact angles on these superhydrophobic surfaces. It was found that Cassie–Baxter equation was valid only for some special pattern geometry. The factors affecting the applicability of the Cassie–Baxter equation such as geometric type of the pillars, size of pillars and separation distance between the pillars are discussed throughout the text.

Combined XPS and contact angle studies of ethylene vinyl acetate and polyvinyl acetate blends

In this study, we prepared thin films by blending ethylene vinyl acetate copolymers (EVA) containing 12–33 (wt.%) vinyl acetate (VA) with polyvinyl acetate (PVAc) and high density polyethylene homopolymers. Large area micropatterns having controlled protrusion sizes were obtained by phase-separation especially for the PVAc/EVA-33 blends using dip coating. These surfaces were characterized by XPS and contact angle measurements. A reasonably linear relation was found between the VA content on the surface (wt.%) obtained from XPS analysis and the VA content in bulk especially for PVAc/EVA-33 blend surfaces. PE segments were more enriched on the surface than that of the bulk for pure EVA copolymer surfaces similar to previous reports and VA enrichment was found on the EVA/HDPE blend surfaces due to high molecular weight of HDPE. Water θ e decreased with the increase in the VA content on the blend surface due to the polarity of VA. A good agreement was obtained between γ s − and atomic oxygen surface concentration with the increase of VA content. The applicability of Cassie–Baxter equation was tested and found that it gave consistent results with the experimental water contact angles for the case where VA content was lower than 55 wt.% in the bulk composition.

A simple method to prepare miniature quartz fiber boats with superhydrophobicity

According to the reformed Cassie–Baxter equation, a superhydrophobic quartz fiber bundle boat was fabricated from mimicking the lotus leaf venation using chemical surface modifications and roughness introductions. Water contact angles as high as 165.8° were achieved for quartz fiber cloths. The loading capacities of the miniature boats made from the superhydrophobic quartz fiber bundles were measured. The highest loading weight, 10.19g, was obtained by the boats with 2.0mm spacing distance between fiber bundles. The striking loading capacities were believed to stem from the air film surrounding the superhydrophobic surfaces of the boats. The results of this study presented new applications of artificial hydrophobic surfaces in areas of aquatic devices.

Laser-Patterned Super-Hydrophobic Pure Metallic Substrates: Cassie to Wenzel Wetting Transitions

A femtosecond laser was used to create microstructures on very pure metal surfaces. The irradiated samples initially showed super-hydrophilic behavior. With time and exposure to ambient air the contact angle increased to about 160° with very low hysteresis. The surfaces supported the Cassie and Wenzel wetting states, depending on the technique used to deposit the water droplets. The created surface morphologies were idealized with a geometric model that is an assembly of densely packed cylindrical pillars with semispherical caps. Using this geometric model for calculation of the surface roughness, a theoretical Young contact angle of about 99° was calculated for all samples from the Wenzel and Cassie–Baxter equations. While the value of 99° significantly differs from the measured hydrophilic contact angles on the polished pure metallic samples, it indicates that a laser-induced surface reaction must be responsible for the evolution of contact angles to super-hydrophobic ones and that this phenomenon is independent of the type of metal.