Analytical modeling and thermodynamic analysis of robust superhydrophobic surfaces with inverse-trapezoidal microstructures

Preparation of Polymer Nanopillar Arrays with Controlled Tip Shapes and Their Application to Hydrophobic and Oleophobic Surfaces

Ordered arrays of nanopillars with controlled tip shapes were fabricated by a template formation process using anodic porous alumina with controlled pore shapes. Although various studies have been reported on the preparation of nanopillar arrays using anodic porous alumina as a template, there have been no reports on the formation of nanopillar arrays with precisely controlled tip shapes. Re-anodization of anodized samples in a neutral electrolyte can flatten the bottom of pores. The use of the resulting anodic porous alumina as a template enabled the fabrication of ordered nanopillar arrays with a flattened tip. The formation of overhanging nanopillar arrays was also possible by using anodic porous alumina with a controlled pore shape as a template, which was fabricated by a combination of anodization, TiO₂ coating by atomic layer deposition, and pore-widening treatment. The contact angles of water and oil droplets were measured using the obtained polymer nanopillar arrays with controlled tip shapes. The contact angle of water droplets did not change regardless of the tip shape of the nanopillars, whereas the contact angle of oil droplets changed depending on the tip shape of the nanopillars. This indicates that liquids with high surface tension are not affected by the nanopillar tip shape, whereas liquids with low surface tension are greatly affected by the nanopillar tip shape. Among the nanopillar arrays fabricated in this study, it was confirmed that the overhanging nanopillar array with many edge structures that have the pinning effect of suppressing the wetting spread of the solution exhibited the highest oil repellency. The method reported here can be used to fabricate nanopillar arrays with a precisely controlled tip geometry, and it is expected that optimization of the geometry will further improve the water- and oil-repellent properties.

Superhydrophobic μ-pillars via simple and scalable SLA 3D-printing: the stair-case effect and their wetting models

In nature, superhydrophobic surfaces (SHSs) exhibit microstructures with several roughness scales. Scalable fabrication and build-up along the X-Y plane represent the promise of 3D printing technology. Herein we report 3D printed microstructures with a dual roughness scale that achieves SHS using a readily available Formlabs stereolithography (SLA) printer. Pillar-like structure (PLS) arrangements with a wide range of geometrical shapes were 3D printed at three resolutions and two printing orientations. We discovered that a tilted printing direction enables a stair-case pattern on the μ-PLS surfaces, conferring them a μ-roughness that reduces the solid-liquid contact area. The programmed resolution governs the number of polymerized layers that give rise to the stepped pattern on the μ-PLS surfaces. However, this is reduced as the printing resolution increases. Also, all samples' experimental contact angles were consistent with theoretical predictions from Cassie-Baxter, Wenzel, and Nagayama wettability models. The underlying mechanisms and governing parameters were also discussed. It is believed that this work will enable scalable and high throughput roughness design in augmenting future 3D printing object applications.

Extended Gibbs Free Energy and Laplace Pressure of Ordered Hexagonal Close-Packed Spherical Particles: A Wettability Study

The wetting property of spherical particles in a hexagonal close-packed (HCP) ordering from extended Gibbs free energy (GFE) and Laplace pressure view points is studied. A formalism is proposed to predict the contact angle (θ) of a droplet on the HCP films and penetration angle (α) of the liquid on the spherical particles. Then, the extended Laplace pressure for the layered HCP ordering is calculated and a correlation between the wetting angle, sign of pressure, and pressure gradient is achieved. Our results show that the sign and the slope of pressure are important criteria for determining the wettability state and it is found that the contact angle is independent of the particle radius, as supported by various experimental reports. The pressure gradient for the HCP films with Young contact angle higher than (lower than) a critical contact angle, 135° (45°), is positive (negative), indicating the superhydrophobicity (superhydrophilicity) state of the surface. To validate the proposed formulation, theoretical calculations are compared with the reported experimental measurements, showing a good agreement.

Surface topographies of biomimetic superamphiphobic materials: design criteria, fabrication and performance

Superamphiphobicity is a wetting phenomenon that not only water but also oils or organic solvents with low surface tension exhibit large contact angles above 150° along with low contact angle hysteresis on solid surface. It is well known that both chemical constituent and surface roughness have impacts on the wettability of solid surface. Herein, several fundamental wetting states and design criteria for re-entrant structures are introduced first. Then, various chemical modification materials endowing solid substrates low surface energy are summarized subsequently. Furthermore, roughening processes conferring hierarchical or re-entrant topographic structures on surfaces are classified based on different types of topographies abstracted from the natural oil-repellent creatures (mushroom-like structures) as well as bio-inspired superamphiphobic surfaces (i.e., randomly distributed nanostructures, regularly patterned microstructures and other complex hierarchical structures). Significantly, the impalement pressure and formulated rules of various re-entrant profiles are recommended in detail. At the same time, fabrication, outstanding performances such as mechanical durability, chemical stability are also mentioned according to different types of morphologies. Beyond that, current fabrication obstacles and future prospects are proposed simultaneously in the end.

Contact angle hysteresis of non-flattened-top micro/nanostructures

A two-dimensional (2D) thermodynamic model is proposed to predict the contact angle (CA) and contact angle hysteresis (CAH) of different types of surface geometries, particularly those with asperities having nonflattened tops. The model is evaluated by micro/nano sinusoidal and parabolic patterns fabricated by laser ablation. These microstructures are analyzed thermodynamically through the use of the Gibbs free energy to obtain the equilibrium contact angle (CA) and contact angle hysteresis (CAH). The effects of the geometrical details of two types of microstructures on maximizing the superhydrophobicity of the nanopatterned surface are also discussed in an attempt to design surfaces with desired and/or optimum wetting characteristics. The analysis of the various surfaces reveals the important geometrical parameters that may lead to the lotus effect (high CA > 150° and low CAH < 10°) or petal effect (high CA > 150° and high CAH ≫ 10°).

Wetting resistance at its topographical limit: the benefit of mushroom and serif T structures

Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in temporarily rain-flooded habitats. They immediately form a plastron, protecting them against suffocation upon immersion into water and even low-surface-tension liquids such as alkanes. Recent experimental studies revealed a high-pressure resistance of such plastrons against collapse. In this work, skin sections of Orthonychiurus stachianus are studied by transmission electron microscopy. The micrographs reveal cavity side-wall profiles with characteristic overhangs. These were fitted by polynomials to allow access for analytical and numerical calculations of the breakthrough pressure, that is, the barrier against plastron collapse. Furthermore, model profiles with well-defined geometries were used to set the obtained results into context and to develop a general design principle for the most robust surface structures. Our results indicate the decisive role of the sectional profile of overhanging structures to form a robust heterogeneous wetting state for low-surface-tension liquids that enables the omniphobicity. Furthermore, the design principles of mushroom and serif T structures pave the way for omniphobic surfaces with a high-pressure resistance irrespective of solid surface chemistry.

Parametric optimization of inverse trapezoid oleophobic surfaces

In this paper, we introduce a comprehensive and versatile approach to the parametric shape optimization of oleophobic surfaces. We evaluate the performance of inverse trapezoid microstructures in terms of three objective parameters: apparent contact angle, maximum sustainable hydrostatic pressure, and mechanical robustness (Im, M.; Im, H:; Lee, J.H.; Yoon, J.B.; Choi, Y.K. A robust superhydrophobic and superoleophobic surface with inverse-trapezoidal microstructures on a large transparent flexible substrate. Soft Matter 2010, 6, 1401-1404; Im, M.; Im, H:; Lee, J.H.; Yoon, J.B.; Choi, Y.K. Analytical Modeling and Thermodynamic Analysis of Robust Superhydrophobic Surfaces with Inverse-Trapezoidal Microstructures. Langmuir 2010, 26, 17389-17397). We find that each of these parameters, if considered alone, would give trivial optima, while their interplay provides a well-defined optimal shape and aspect ratio. The inclusion of mechanical robustness in combination with conventional performance characteristics favors solutions relevant for practical applications, as mechanical stability is a critical issue not often addressed in idealized models.

The Cassie equation: how it is meant to be used

A review of literature shows that the majority of papers cite a potentially incorrect form of the Cassie and Cassie-Baxter equations to interpret or predict contact angle data. We show that for surfaces wet with a composite interface, the commonly used form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ-(1-f), is only correct for the case of flat topped pillar geometry without any penetration of the liquid. In general, the original form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ(1)-f(2), with f(1)+f(2)≥1, should be used. The differences between the two equations are discussed and the errors involved in using the incorrect equation are estimated to be between ~3° and 13° for superhydrophobic surfaces. The discrepancies between the two equations are also discussed for the case of a liquid undergoing partial, but increasing, levels of penetration. Finally, a general equation is presented for the transition/stability criterion between the Cassie-Baxter and Wenzel modes of wetting.

Methodology for imaging nano-to-microscale water condensation dynamics on complex nanostructures

A better understanding of the role that nanoscale surface chemical heterogeneities and topographical features play in water droplet formation is necessary to improve design and robustness of nanostructured superhydrophobic surfaces as to make them fit for industrial applications. Lack of an imaging method capable of capturing the water condensation process on complex nanostructures with required magnification has thus far hindered experimental progress in this area. In this work, we demonstrate that by transferring a small part of a macroscale sample to a novel thermally insulated sample platform we are able to mitigate flooding and electron heating problems typically associated with environmental scanning electron microscopy of water condensation. We image condensation dynamics on individual complex particles and a superhydrophobic network of nanostructures fabricated from low thermal conductivity materials with an unobstructed 90° perspective of the surface-to-water interface with field of view as small as 1 μm(2). We clearly observe the three-stage drop growth process and demonstrate that even during late stages of the droplet growth the nearly spherical drop remains in a partially wetting Wenzel state.

Theoretical consideration of wetting on a cylindrical pillar defect: pinning energy and penetrating phenomena

Wetting on a cylindrical pillar defect is discussed in terms of the free-energy difference ΔG. Wetting is divided into wetting on a flat surface, a pinning effect at the apex of the defect, and wetting on a pillar wall. First, we confirmed that ΔG between before and after ideal wetting on a flat surface can be derived as a function of the contact angle θ in which the free-energy minimum is obtained as the equilibrium contact angle θ(eq) described by Young's and Wenzel's laws. Second, the pinning effect at the apex in the cross section of the pillar defect is discussed in ΔG, where the pinning effect is shown to originate from the energy barrier by an increase in the air-liquid interfacial area of a pinned droplet induced by deformation. Next, the ΔG profiles of wetting on the pillar wall are drawn based on the theory of Carroll (Carroll, B. J. J. Colloid Interface Sci.1976, 57, 488-495) to better understand the ΔG profile during penetration. Differences in the manner of wetting between the wetting state on a flat surface and the pillar wall are reflected in ΔG. Finally, penetration of a droplet into a pillar defect is comprehensively discussed on the basis of wetting on a flat surface and a pillar wall. If we consider a simple manner of penetration, another type of energy barrier resulting from an anomalous deformation of the air-liquid interface of the penetrating droplet can be theoretically suggested. Consequently, two types of energy barrier are found. These energy barriers should play a significant role in the hysteresis of wetting, the liquid-repellent Cassie-Baxter state (CB), and the CB-Wenzel wetting transition on a microtextured surface.