Hydrophobic properties of a wavy rough substrate

Frictionless multiphasic interface for near-ideal aero-elastic pressure sensing

Conventional pressure sensors rely on solid sensing elements. Instead, inspired by the air entrapment phenomenon on the surfaces of submerged lotus leaves, we designed a pressure sensor that uses the solid-liquid-liquid-gas multiphasic interfaces and the trapped elastic air layer to modulate capacitance changes with pressure at the interfaces. By creating an ultraslippery interface and structuring the electrodes at the nanoscale and microscale, we achieve near-friction-free contact line motion and thus near-ideal pressure-sensing performance. Using a closed-cell pillar array structure in synergy with the ultraslippery electrode surface, our sensor achieved outstanding linearity (R2 = 0.99944 ± 0.00015; nonlinearity, 1.49 ± 0.17%) while simultaneously possessing ultralow hysteresis (1.34 ± 0.20%) and very high sensitivity (79.1 ± 4.3 pF kPa-1). The sensor can operate under turbulent flow, in in vivo biological environments and during laparoscopic procedures. We anticipate that such a strategy will enable ultrasensitive and ultraprecise pressure monitoring in complex fluid environments with performance beyond the reach of the current state-of-the-art.

Study of Micro- and Nanopatterned Aluminum Surfaces Using Different Microfabrication Processes for Water Management

Superhydrophobic surfaces demonstrate extreme water-repellence, promoting drop-wise over film-wise condensation, increasing liquid mobility, and reducing thermal resistance for heat-exchanger applications. Introducing topographic structures can lead to modified surface free energy, as inspired by natural systems like the lotus leaf, potentially allowing coating-free ice- and frost-free surfaces under certain conditions. This work presents a study of coating-free aluminum micro/nanopatterns fabricated using micromilling or laser-etching techniques and the resultant wetting properties. Our review and experiments clarify the roles of line-edge-roughness and microstructural geometry from each microfabrication technique, which manifests in technique-specific nano- to midmicro-scale roughness, producing a hierarchical structure in both cases. For micromilling, line-edge-roughness consists of jagged burrs of 1-8 μm thickness with 10-25 μm periodicity along the microlines with constantly changing height on the order of 1-20 μm. These effects simultaneously raise the water contact angle from 52° (unprocessed aluminum) up to 136° but with strong edge pinning effects. On the other hand, laser-etched surfaces exhibit line-edge-roughness with a microstructure of 3-20 μm width and 5-10 μm in height superimposed with evenly spread spikes of 50-250 nm. This results in a high contact angle (>150°) coupled with a low contact angle hysteresis (<15°), promoting superhydrophobicity on a coating-free aluminum surface. It is also shown that for certain cases, line-edge-roughness is more important for the resultant wetting properties than the structure geometry.

Skin hydrophobicity as an adaptation for self-cleaning in geckos

Hydrophobicity is common in plants and animals, typically caused by high relief microtexture functioning to keep the surface clean. Although the occurrence and physical causes of hydrophobicity are well understood, ecological factors promoting its evolution are unclear. Geckos have highly hydrophobic integuments. We predicted that, because the ground is dirty and filled with pathogens, high hydrophobicity should coevolve with terrestrial microhabitat use. Advancing contact-angle (ACA) measurements of water droplets were used to quantify hydrophobicity in 24 species of Australian gecko. We reconstructed the evolution of ACA values, in relation to microhabitat use of geckos. To determine the best set of structural characteristics associated with the evolution of hydrophobicity, we used linear models fitted using phylogenetic generalized least squares (PGLS), and then model averaging based on AICc values. All species were highly hydrophobic (ACA > 132.72°), but terrestrial species had significantly higher ACA values than arboreal ones. The evolution of longer spinules and smaller scales was correlated with high hydrophobicity. These results suggest that hydrophobicity has coevolved with terrestrial microhabitat use in Australian geckos via selection for long spinules and small scales, likely to keep their skin clean and prevent fouling and disease.

Thermodynamic analysis on wetting states and wetting state transitions of rough surfaces

Determining the equilibrium wetting states and exploring the conditions and mechanisms of the wetting state transition from the Cassie-Baxter (CB) state to the Wenzel (W) state (CB-W transition) have been a central topic in the study of superhydrophobic behavior on rough or textured surfaces. Although considerable progress has been made, some issues regarding this topic are still not completely understood. In this study, a systematic thermodynamic analysis has been performed to address several key issues related to this topic. Generalized theoretical expressions for determining the equilibrium wetting states (the threshold Young contact angle of the CB region) and evaluating the stability of the CB state (the energy barrier separating the CB and W states and the critical pressure for the CB-W transition) have been derived. Applying these expressions to four types of surfaces built with protrusions in paraboloid, truncated cone, inverted truncated cone and flat-top pillar shapes, the wetting equilibrium and resultant wetting states have been studied. The physical meanings of the threshold Young contact angle, the roles and mechanisms of the energy barrier and critical pressure in stabilizing the CB state have been discussed. Finally, a general guidance for achieving robust superhydrophobicity on the studied surfaces has been given.

Influence of surface topography attributes on settlement and adhesion of natural and synthetic species

Surface topographies of various sizes, shapes, and spatial organization abound in nature. They endow properties such as super-hydrophobicity, reversible adhesion, anti-fouling, self-cleaning, anti-glare, and anti-bacterial, just to mention a few. Researchers have long attempted to replicate these structures to create artificial surfaces with the functionalities found in nature. In this review, we decompose the attributes of surface topographies into their constituents, namely feature dimensions, geometry, and stiffness, and examine how they contribute (individually or collectively) to settlement and adhesion of natural organisms and synthetic particles on the surface. The size of features that comprise the topography affects the contact area between the particle and surface as well as its adhesion and contributes to the observed adsorptive properties of the surface. The geometry of surface perturbations can also affect the contact area and gives rise to anisotropic particle settlement. Surface topography also affects the local stiffness of the surface and governs the adhesion strength on the surface. Overall, systematically studying attributes of surface topography and elucidating how each of them affects adhesion and settlement of particles will facilitate the design of topographically-corrugated surfaces with desired adsorption characteristics.

Influence of long-range forces and capillarity on the function of underwater superoleophobic wrinkled surfaces

Underwater superoleophobic surfaces can be considered a particular type of lubricant-infused surface, that have anti-fouling properties by virtue of a trapped water layer that repels oils. However, as their function relies on a water layer being trapped in the surface roughness, it is crucial to understand the factors that determine the layer stability. In this work, the forces that are responsible for the stability of thin liquid films within structured surfaces were quantified, and the conclusions were tested against the performance of wrinkled surfaces as underwater superoleophobic coatings. Here, the system studied was a family of wrinkled surfaces made of hydrophilic poly(4-vinylpyridine) (P4VP), whereby the wrinkle width could be controllably tuned in the range 90 nm to 8000 nm. The van der Waals free energy was quantified and the capillary forces trapping water in the surface micro- and nano-wrinkle structure were estimated. P4VP surfaces with micro-scale wrinkles had underwater superoleophobic properties, and low adhesion to different oils with droplet roll-off angle below 6° ± 1°. Despite the van der Waals free energy of the system pointing to the dewetting of a water film under oil on top of a smooth P4VP film, the wrinkled structure is sufficient to induce a Cassie state with a trapped water layer. The micro-scale wrinkles (average width 4-12 μm) were found to be particularly effective in the trapping of the water in a Cassie non-adhesive state. The P4VP wrinkled surfaces are superamphiphobic, as when they were first infused with oil, and then exposed to a droplet of water under oil, they exhibited superhydrophobic behavior. The P4VP wrinkles have the additional useful feature of being transparent underwater, which makes them useful candidates for the protection of underwater cameras and sensors.

Probing Liquid-Solid and Vapor-Liquid-Solid Interfaces of Hierarchical Surfaces Using High-Resolution Microscopy

Liquid-solid (LS) and vapor-liquid-solid (VLS) interfaces are important for the fundamental understanding of how surface chemistry impacts industrial processes and applications. Superhydrophobic surfaces, from structural hierarchies, were fabricated by coating flat smooth surfaces with hollow glass microspheres. These surfaces are referred to as structural hierarchical-modified microsphere surfaces (SHiMMs). Two-phase LS and three-phase VLS interfaces of water droplets on SHiMMs, with an apparent static contact angle (aSCA) of ∼160°, were probed at microscale using environmental scanning electron microscopy (ESEM) and high-resolution optical microscopy (OM). Both ESEM and OM confirmed the presence of air pockets in 3-150 μm range at the VLS triple-phase of the droplet peripheral contact line. The wetting characteristics of the LS interface in the interior of the water droplet were probed using energy-dispersive spectroscopy, which corroborated well with the VLS triple-phase observations, confirming the presence of both the microscale air pockets and fractional complete wetting of the SHiMMs. The superhydrophobic water droplets on the SHiMMs also exhibited relatively high adhesion to the SHiMMs-a tilt angle of 10°-40° was needed for detaching the droplets off the surfaces. Semiquantitative three-phase contact-line analysis and experimental data indicated high-water aSCA, and large adhesion on the microscale-roughened SHiMMs is attributed to pinning of the probe liquid both at the triple VLS and interior LS interfaces. The control over microroughness and surface chemistry of the SHiMMs will allow tuning of both the static and dynamic liquid-surface interactions.

Effect of drop volume and surface statistics on the superhydrophobicity of randomly rough substrates

In this paper, a simple theoretical approach is developed with the aim of evaluating shape, interfacial pressure, apparent contact angle and contact area of liquid drops gently deposed on randomly rough surfaces. This method can be useful to characterize the superhydrophobic properties of rough substrates, and to investigate the contact behavior of impacting drops. We assume that (i) the size of the apparent liquid-solid contact area is much larger than the micromorphology of the substrate, and (ii) a composite interface is always formed at the microscale. Results show apparent contact angle and liquid-solid area fraction are slightly influenced by the drop volume only at relatively high values of the root mean square roughness h _rms, whereas the effect of volume is practically negligible at small h _rms. The main statistical quantity affecting the superhydrophobic properties is found to be the Wenzel roughness parameter r _W, which depends on the average slope of the surface heights. Moreover, transition from the Cassie-Baxter state to the Wenzel one is observed when r _W reduces below a certain critical value, and theoretical predictions are found to be in good agreement with experimental data. Finally, the present method can be conveniently exploited to evaluate the occurrence of pinning phenomena in the case of impacting drops, as the Wenzel critical pressure for liquid penetration gives an estimation of the maximum impact pressure tolerated by the surface without pinning occurring.

Fluid contact angle on solid surfaces: Role of multiscale surface roughness

We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.

Statistical theory of wetting of liquid drops on superhydrophobic randomly rough surfaces

It is well known that hydrophobic surfaces may become superhydrophobic when their surface is properly roughened. However, the role of roughness is not yet very clear, notwithstanding several theoretical and experimental investigations. In the present paper, we propose a relatively simple theory aiming at calculating the apparent contact angle (ACA) and the contact area occurring in the case of drops gently deposited on two-dimensional randomly rough surfaces. Our theory applies both to isotropic and anisotropic rough surfaces, although in the latter case the predicted ACA has to be interpreted as the average contact angle at the triple line. We assume large separation of scales, i.e., that the spectral content of the surface lies in a range of wavelengths much smaller than the size of the apparent liquid-solid contact area. Results show that anisotropy negligibly affects the ACA, and a very reasonable agreement is obtained between theoretical ACA values and experimental data.

An effective medium approach to predict the apparent contact angle of drops on super-hydrophobic randomly rough surfaces

The apparent contact angle of large 2D drops with randomly rough self-affine profiles is numerically investigated. The numerical approach is based upon the assumption of large separation of length scales, i.e. it is assumed that the roughness length scales are much smaller than the drop size, thus making it possible to treat the problem through a mean-field like approach relying on the large-separation of scales. The apparent contact angle at equilibrium is calculated in all wetting regimes from full wetting (Wenzel state) to partial wetting (Cassie state). It was found that for very large values of the roughness Wenzel parameter (r(W) > -1/ cos θ(Y), where θ(Y) is the Young's contact angle), the interface approaches the perfect non-wetting condition and the apparent contact angle is almost equal to 180°. The results are compared with the case of roughness on one single scale (sinusoidal surface) and it is found that, given the same value of the Wenzel roughness parameter rW, the apparent contact angle is much larger for the case of a randomly rough surface, proving that the multi-scale character of randomly rough surfaces is a key factor to enhance superhydrophobicity. Moreover, it is shown that for millimetre-sized drops, the actual drop pressure at static equilibrium weakly affects the wetting regime, which instead seems to be dominated by the roughness parameter. For this reason a methodology to estimate the apparent contact angle is proposed, which relies only upon the micro-scale properties of the rough surface.

The effect of drop volume and micropillar shape on the apparent contact angle of ordered microstructured surfaces

In the present paper, we propose a new theoretical approach to evaluate the shape and apparent contact angle (ACA) of a drop gently deposited on microstructured superhydrophobic surfaces. We exploit the very large separation of scales between the drop size and the features of the micromorphology of the interface to propose a numerical methodology to calculate the apparent contact area and apparent contact angle. In agreement with very recent experiments, calculations show that, in the case of surfaces made of conical micropillars, the ACA may take values very close to 180° not depending on the size of the liquid drop. At large drop volumes, the shape of the drop deviates from the spherical one as a result of the gravity effects, but it is noteworthy that the apparent contact angle does not change at all. Our calculations shows that this holds true also for different pillar shapes, showing that, for any given Young contact angle of the solid constituting the pillars, the ACA is an intrinsic property of the surface microgeometry.

25th anniversary article: scalable multiscale patterned structures inspired by nature: the role of hierarchy

Multiscale, hierarchically patterned surfaces, such as lotus leaves, butterfly wings, adhesion pads of gecko lizards are abundantly found in nature, where microstructures are usually used to strengthen the mechanical stability while nanostructures offer the main functionality, i.e., wettability, structural color, or dry adhesion. To emulate such hierarchical structures in nature, multiscale, multilevel patterning has been extensively utilized for the last few decades towards various applications ranging from wetting control, structural colors, to tissue scaffolds. In this review, we highlight recent advances in scalable multiscale patterning to bring about improved functions that can even surpass those found in nature, with particular focus on the analogy between natural and synthetic architectures in terms of the role of different length scales. This review is organized into four sections. First, the role and importance of multiscale, hierarchical structures is described with four representative examples. Second, recent achievements in multiscale patterning are introduced with their strengths and weaknesses. Third, four application areas of wetting control, dry adhesives, selectively filtrating membranes, and multiscale tissue scaffolds are overviewed by stressing out how and why multiscale structures need to be incorporated to carry out their performances. Finally, we present future directions and challenges for scalable, multiscale patterned surfaces.

Role of statistical properties of randomly rough surfaces in controlling superhydrophobicity

We investigate the effect of statistical properties of the surface roughness on its superhydrophobicity. In particular, we focus on the liquid-solid interfacial structure and its dependence on the coupled effect of surface statistical properties and drop pressure. We find that, for self-affine fractal surfaces with Hurst exponent H > 0.5, the transition to the Wenzel state first involves the short wavelengths of the roughness and, then, gradually moves to larger and larger scales. However, as the drop pressure is increased, at a certain point of the loading history, an abrupt transition to the Wenzel state occurs. This sudden transition identifies the critical drop pressure p(W), which destabilizes the composite interface. We find that p(W) can be strongly enhanced by increasing the mean square slope of the surface, or equivalently the Wenzel roughness parameter r(W). Our investigation shows that, even in the case of randomly rough surface, r(W) is still the most crucial parameter in determining the superhydrophobicity of the surface. An analytical approach is, then, proposed to show that, for any given value of Young's contact angle θ(Y), a threshold value (r(W))(th) = 1/(-cos θ(Y)) exists, above which the composite interface is strongly stabilized and the surface presents robust superhydrophobic properties. Interestingly, this threshold value is identical to the one that would be obtained in pure Wenzel regime to guarantee perfect superhydrophobicity.

Biomimetic surfaces with controlled direction-dependent adhesion

We propose a novel design of a biomimetic micro-structured surface, which exhibits controlled strongly direction-dependent adhesion properties. The micro-system consists of parallel elastic wall-like structures covered by a thin layer. Numerical calculations have been carried out to study the adhesive properties of the proposed system and to provide design criteria with the aim of obtaining optimized geometries. A numerically equivalent version of the double cantilever beam fracture experiment is, then, simulated by means of finite element analysis to investigate the anisotropic adhesion of the structure. We find that, because of inherent crack trapping properties of these types of structures, the wall-like geometry allows us to strongly enhance adhesion when the detachment direction is perpendicular to the walls. On the other hand, when the detachment occurs parallel to the walls, the system shows low adhesion. This controlled direction-dependent adhesive property of the proposed structure solves one of the key problems of biomimetic adhesive surfaces, which usually show very strong adhesion, even larger than biological systems, but are not suitable for object manipulation and locomotion, as detachment always occurs at high loads and cannot be controlled.

Wenzel and Cassie-Baxter states of an electrolytic drop on charged surfaces

In this paper, we provide a theory for the Wenzel and the Cassie-Baxter states of an electrolyte drop on charged surfaces. An electric double layer (EDL) develops when the electrolyte drop comes in contact with the charged surface. Therefore, the EDL free energy affects these states by triggering a hydrophilicity-inducing tendency. Consequently, an originally hydrophilic condition leads to a superhydrophilic Wenzel state, and an originally hydrophobic condition leads to a less hydrophobic Wenzel state. For the Cassie-Baxter state, this gives rise to the most remarkable situation of a hydrophilic (as compared to the original) Cassie-Baxter state.

Molecular dynamics simulation study of interaction between model rough hydrophobic surfaces

We study some aspects of hydrophobic interaction between molecular rough and flexible model surfaces. The model we use in this work is based on a model we used previously (Eun, C.; Berkowitz, M. L. J. Phys. Chem. B 2009, 113, 13222-13228), when we studied the interaction between model patches of lipid membranes. Our original model consisted of two graphene plates with attached polar headgroups; the plates were immersed in a water bath. The interaction between such plates can be considered as an example of a hydrophilic interaction. In the present work, we modify our previous model by removing the charge from the zwitterionic headgroups. As a result of this procedure, the plate character changes: it becomes hydrophobic. By separating the total interaction (or potential of mean force, PMF) between plates into the direct and the water-mediated interactions, we observe that the latter changes from repulsive to attractive, clearly emphasizing the important role of water as a medium. We also investigate the effect of roughness and flexibility of the headgroups on the interaction between plates and observe that roughness enhances the character of the hydrophobic interaction. The presence of a dewetting transition in a confined space between charge-removed plates confirms that the interaction between plates is strongly hydrophobic. In addition, we notice that there is a shallow local minimum in the PMF in the case of the charge-removed plates. We find that this minimum is associated with the configurational changes that flexible headgroups undergo as the two plates are brought together.

The influence of molecular-scale roughness on the surface spreading of an aqueous nanodrop

We examine the effect of nanoscale roughness on spreading and surface mobility of water nanodroplets. Using molecular dynamics, we consider model surfaces with sub-nanoscale asperities at varied surface coverage and with different distribution patterns. We test materials that are hydrophobic, and those that are hydrophilic in the absence of surface corrugations. Interestingly, on both types of surfaces, the introduction of surface asperities gives rise to a sharp increase in the apparent contact angle. The Cassie-Baxter equation is obeyed approximately on hydrophobic substrates, however, the increase in the contact angle on a hydrophilic surface differs qualitatively from the behavior on macroscopically rough surfaces described by the Wenzel equation. On the hydrophobic substrate, the superhydrophobic state with the maximal contact angle of 180 degrees is reached when the asperity coverage falls below 25%, suggesting that superhydrophobicity can also be achieved by the nanoscale roughness of a macroscopically smooth material. We further examine the effect of surface roughness on droplet mobility on the substrate. The apparent diffusion constant shows a dramatic slow down of the nanodroplet translation even for asperity coverage in the range of 1% for a hydrophilic surface, while droplets on corrugated hydrophobic surfaces retain the ability to flow around the asperities. In contrast, for smooth surfaces we find that the drop mobility on the hydrophilic surface exceeds that on the hydrophobic one.

Thermodynamic analysis of the effect of the hierarchical architecture of a superhydrophobic surface on a condensed drop state

Condensed drops usually display a Wenzel state on a superhydrophobic surface (SHS) only with microrough architecture, while Cassie drops easily appear on a surface with micro-nano hierarchical roughness. The mechanism of this is not very clear. It is important to understand how the hierarchical structure affects the states of condensation drops so that a good SHS can be designed to achieve the highly efficient dropwise condensation. In this study, the interface free energy (IFE) of a local condensate, which comes from the growth and combination of numerous initial condensation nuclei, was calculated during its shape changes from the early flat shape to a Wenzel or Cassie state. The final state of a condensed drop was determined by whether the IFE continuously decreased or a minimum value existed. The calculation results indicate that the condensation drops on the surface only with microroughness display a Wenzel state because the IFE curve of a condensed drop first decreases and then increases, existing at a minimum value corresponding to a Wenzel drop. On a surface with proper hierarchical roughness, however, the interface energy curve of a condensed drop will continuously decline until reaching a Cassie state. Therefore, a condensed drop on a hierarchical roughness surface can spontaneously change into a Cassie state. Besides, the states and apparent contact angles of condensed drops on a SHS with different structural parameters published in the literature were calculated and compared with experimental observations. The results show that the calculated condensed drop states are well-coordinated with experimental clarifications. We can conclude that micro-nano hierarchical roughness is the key structural factor for sustaining condensed drops in a Cassie state on a SHS.

Microstructured superhydrorepellent surfaces: effect of drop pressure on fakir-state stability and apparent contact angles

In this paper we present a generalized Cassie-Baxter equation to take into account the effect of drop pressure on the apparent contact angle θ(app). Also we determine the limiting pressure p(W) which causes the impalement transition to the Wenzel state and the pull-off pressure p(out) at which the drop detaches from the substrate. The calculations have been carried out for axial-symmetric pillars of three different shapes: conical, hemispherical-topped and flat-topped cylindrical pillars. Calculations show that, assuming the same pillar spacing, conical pillars may be more inclined to undergo an impalement transition to the Wenzel state, but, on the other hand, they are characterized by a vanishing pull-off pressure which causes the drop not to adhere to the substrate and therefore to detach very easily. We infer that this property should strongly reduce the contact angle hysteresis as experimentally observed in Martines et al (2005 Nano Lett. 5 2097-103). It is possible to combine large resistance to impalement transition (i.e. large value of p(W)) and small (or even vanishing) detaching pressure p(out) by employing cylindrical pillars with conical tips. We also show that, depending on the particular pillar geometry, the effect of drop pressure on the apparent contact angle θ(app) may be more or less significant. In particular we show that in the case of conical pillars increasing the drop pressure causes a significant decrease of θ(app) in agreement with some experimental investigations (Lafuma and Quéré 2003 Nat. Mater. 2 457), whereas θ(app) slightly increases for hemispherical or flat-topped cylindrical pillars.

Small droplets on superhydrophobic substrates

We investigate the wetting behavior of liquid droplets on rough hydrophobic substrates for the case of droplets that are of comparable size to the surface asperities. Using a simple three-dimensional analytical free-energy model, we have shown in a recent letter [M. Gross, F. Varnik, and D. Raabe, EPL 88, 26002 (2009)] that, in addition to the well-known Cassie-Baxter and Wenzel states, there exists a further metastable wetting state where the droplet is immersed into the texture to a finite depth, yet not touching the bottom of the substrate. Due to this new state, a quasistatically evaporating droplet can be saved from going over to the Wenzel state and instead remains close to the top of the surface. In the present paper, we give an in-depth account of the droplet behavior based on the results of extensive computer simulations and an improved theoretical model. In particular, we show that releasing the assumption that the droplet is pinned at the outer edges of the pillars improves the analytical results for larger droplets. Interestingly, all qualitative aspects, such as the existence of an intermediate minimum and the "reentrant transition," remain unchanged. We also give a detailed description of the evaporation process for droplets of varying sizes. Our results point out the role of droplet size for superhydrophobicity and give hints for achieving the desired wetting properties of technically produced materials.

Nano to micro structural hierarchy is crucial for stable superhydrophobic and water-repellent surfaces

Water-repellent biological systems such as lotus leaves and water strider's legs exhibit two-level hierarchical surface structures with the smallest characteristic size on the order of a few hundreds nanometers. Here we show that such nano to micro structural hierarchy is crucial for a superhydrophobic and water-repellent surface. The first level structure at the scale of a few hundred nanometers allows the surface to sustain the highest pressure found in the natural environment of plants and insects in order to maintain a stable Cassie state. The second level structure leads to dramatic reduction in contact area, hence minimizing adhesion between water and the solid surface. The two level hierarchy further stabilizes the superhydrophobic state by enlarging the energy difference between the Cassie and the Wenzel states. The stability of Cassie state at the nanostructural scale also allows the higher level structures to restore superhydrophobicity easily after the impact of a rainfall.

Coexistence and transition between Cassie and Wenzel state on pillared hydrophobic surface

Water droplets on rugged hydrophobic surfaces typically exhibit one of the following two states: (i) the Wenzel state [Wenzel RN (1936) Ind Eng Chem 28:988-994] in which water droplets are in full contact with the rugged surface (referred as the wetted contact) or (ii) the Cassie state [Cassie, ABD, Baxter S (1944) Trans Faraday Soc 40:546-551] in which water droplets are in contact with peaks of the rugged surface as well as the "air pockets" trapped between surface grooves (the composite contact). Here, we show large-scale molecular dynamics simulation of transition between Wenzel state and Cassie state of water droplets on a periodic nanopillared hydrophobic surface. Physical conditions that can strongly affect the transition include the height of nanopillars, the spacing between pillars, the intrinsic contact angle, and the impinging velocity of water nanodroplet ("raining" simulation). There exists a critical pillar height beyond which water droplets on the pillared surface can be either in the Wenzel state or in the Cassie state, depending on their initial location. The free-energy barrier separating the Wenzel and Cassie state was computed on the basis of a statistical-mechanics method and kinetic raining simulation. The barrier ranges from a few tenths of k(B)T(0) (where k(B) is the Boltzmann constant, and T(0) is the ambient temperature) for a rugged surface at the critical pillar height to approximately 8 k(B)T(0) for the surface with pillar height greater than the length scale of water droplets. For a highly rugged surface, the barrier from the Wenzel-to-Cassie state is much higher than from Cassie-to-Wenzel state. Hence, once a droplet is trapped deeply inside the grooves, it would be much harder to relocate on top of high pillars.

Superhydrophobicity of boron nitride nanotubes grown on silicon substrates

Partially vertical aligned boron nitride nanotubes (BNNTs) on Si substrates are found to be superhydrophobic in contrast to boron nitride (BN) thin films. While the hexagonal-phase BN films are partially wetted by water with advancing contact angle of about 50 degrees , partially vertically aligned BNNTs can achieve superhydrophobic state with advancing water contact angle exceeding 150 degrees . Our results show that the pH value of water does not affect the wetting characteristics of BNNTs. Since BN is chemically inert, resistive to oxidation up to 900 degrees C, and transparent to visible-UV light, BNNTs could potentially be useful as self-cleaning, transparent, insulating, anticorrosive coatings under rigorous chemical and thermal conditions.

Nanodroplets on rough hydrophilic and hydrophobic surfaces

We present results of Molecular Dynamics (MD) calculations on the behavior of liquid nanodroplets on rough hydrophobic and hydrophilic solid surfaces. On hydrophobic surfaces, the contact angle for nanodroplets depends strongly on the root-mean-square roughness amplitude, but it is nearly independent of the fractal dimension of the surface. Since increasing the fractal dimension increases the short-wavelength roughness, while the long-wavelength roughness is almost unchanged, we conclude that for hydrophobic interactions the short-wavelength (atomistic) roughness is not very important. We show that the nanodroplet is in a Cassie-like state. For rough hydrophobic surfaces, there is no contact angle hysteresis due to strong thermal fluctuations, which occur at the liquid-solid interface on the nanoscale. On hydrophilic surfaces, however, there is strong contact angle hysteresis due to higher energy barrier. These findings may be very important for the development of artificially biomimetic superhydrophobic surfaces.

Life and death of a fakir droplet: impalement transitions on superhydrophobic surfaces

We show that the equilibrium state of a water drop deposited on a superhydrophobic surface cannot be solely determined by its macroscopic contact angle but also depends on the drop size. Following the evolution of the interface of evaporating droplets, we demonstrate that the liquid can explore a succession of equilibrium conformations which are neither of the usual fakir nor Wenzel types. A comprehensive description of the transition between these wetting states is provided. To do so, we have taken advantage of microfabrication techniques and interference microscopy which allows for the "3D" imaging of the liquid interface. In addition, we propose a simple theoretical description of the interface geometry which goes beyond the standard two-state picture for superhydrophobicity. This model accounts correctly for all our experimental observations. Finally, guided by potential microfluidic applications we propose an efficient design strategy to build robust liquid repellant surfaces.

Anisotropic wetting on tunable micro-wrinkled surfaces

We examine the wettability of rough surfaces through a measurement approach that harnesses a wrinkling instability to produce model substrate topographies. Specifically, we probe the wetting of liquids on anisotropic micro-wrinkled features that exhibit well-defined aspect ratios (amplitude wavelength of the wrinkles) that can be actively tuned. Our study provides new insight into the wetting behavior on rough surfaces and into the interpretation of related liquid contact-angle measurements. In particular, we find that droplet wetting anisotropy is governed primarily by the roughness aspect ratio. In addition, comparison of our measurements to theoretical models demonstrates that droplet distortions and observed contact angles on surfaces with a strongly anisotropic texture can be quantitatively attributed to the difference in the energetic barriers to wetting along and perpendicular to substrate features.

Mechanical and superhydrophobic stabilities of two-scale surfacial structure of lotus leaves

To understand why lotus leaf surfaces have a two-scale structure, we explore in this paper two stability mechanisms. One is the stability of the Cassie-Baxter wetting mode that generates the superhydrophobicity. A recent quantitative study (Zheng et al., Langmuir 2005, 21, 12207) showed that the larger the slenderness ratio of the surface structures was, the more stable the Cassie-Baxter wetting mode would be. On the other hand, it is well-known that more slender surface structures can only sustain lower critical water pressures for structure buckling, or Euler instability, while in the natural environments, the water pressure impacting on the lotus surface can reach a fairly high value (105 Pa in a heavy rain). Our analysis reveals that the two-scale structure of the lotus leaf surfaces is necessary for keeping both the structure and the superhydrophobicity stable. Furthermore, we find that the water-air interfacial tension makes the slender surface structure more instable and the two-scale structure a necessity.

Microtextured superhydrophobic surfaces: a thermodynamic analysis

Superhydrophobic surfaces with a contact angle (CA) larger than 150 degrees have recently attracted great interest in both academic research and practical applications due to their water-repellent or self-cleaning properties. However, thermodynamic mechanisms responsible for the effects of various factors such as surface geometry and chemistry, liquids, and environmental sources have not been well understood. In this study, a pillar microtexture, which has been intensively investigated in experiments, is chosen as a typical example and thermodynamically analyzed in detail. To gain a comprehensive insight into superhydrophobic behavior, the roles of pillar height, width and spacing (or roughness and solid fraction), intrinsic CA, drop size, and vibrational energy are systematically investigated. Free energy (FE) and free energy barrier (FEB) are calculated using a simple and robust model. Based on the calculations of FE and FEB, various CAs, including apparent, equilibrium (stable), advancing and receding CAs, and contact angle hysteresis (CAH) can be determined. Especially, the design of practical superhydrophobic surfaces is emphasized in connection with the transition between noncomposite and composite states; a criterion for judging such transition is proposed. The theoretical results are consistent with the Wenzel's and the Cassie's equations for equilibrium CA values and experimental observations. Furthermore, based on these results and the proposed criterion, some general principles to achieve superhydrophobic performance are suggested.

Application of superhydrophobic edge effects in solving the liquid outflow phenomena

In this paper, we discuss various edge effects on the outflow behaviors of water around the edge to solve the troublesome problem that frequently brings about great inconvenience in daily lives. A simple method of pressing a drop over the edges of a conical frustum was adopted here to explore the stability of a suspended drop around the edges. On the basis of experiments and theoretical analyses, the critical pressure P(c) and the pressing work DeltaE(w) were used for characterizing the stability of water around an edge, which were found to be closely related to the geometric morphologies, the microstructures of sides, and the material characteristics. The stability of suspended drops around the edge may be enhanced by increasing the rise angle omega, the actual rise angle phi, and the size of edge circles and by using low surface energy materials. Thus, a facile and effective strategy has been successfully developed. We believe that these findings will help to design novel tubes and bottles without a liquid outflow problem.

Porous silicon protein microarray technology and ultra-/superhydrophobic states for improved bioanalytical readout

One attractive method for monitoring biomolecular interactions in a highly parallel fashion is the use of microarrays. Protein microarray technology is an emerging and promising tool for protein analysis, which ultimately may have a large impact in clinical diagnostics, drug discovery studies and basic protein research. This chapter is based upon several original papers presenting our effort in the development of new protein microarray chip technology. The work describes a novel 3D surface/platform for protein characterization based on porous silicon. The simple adjustment of pore morphology and geometry offers a convenient way to control wetting behavior of the microarray substrates. In this chapter, an interesting insight into the surface role in bioassays performance is made. The up-scaled fabrication of the novel porous chips is demonstrated and stability of the developed supports as well as the fluorescent bioassay reproducibility and data quality issues are addressed. We also describe the efforts made by our group to link protein microarrays to matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS), suggesting porous silicon as a convenient platform for fast on-surface protein digestion protocols linked to MS-readout. The fabrication of ultra- and superhydrophobic states on porous silicon is also described and the utilization of these water-repellent properties for a new microscaled approach to superhydrophobic MALDI-TOF MS target anchor chip is covered.

Superhydrophobic effects of self-assembled monolayers on micropatterned surfaces: 3-D arrays mimicking the lotus leaf

The contact angle of water has been measured on a series of self-assembled monolayers (SAM) on thermally evaporated and sputter coated silver surfaces. It is found that micropatterning the surface using nanosphere lithography leads to large increases in the contact angle and generates superhydrophobic surfaces with contact angles >150 degrees. The type of functional groups on the SAMs, the metal island size, and the metal island thickness all contribute to the measured contact angle. The maximum contact angle found was 161 degrees for a fluorinated alkanethiol on 80 nm thick silver islands.

Influence of surface roughness on superhydrophobicity

Superhydrophobic surfaces, with a liquid contact angle theta greater than 150 degrees , have important practical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. Many biological surfaces, such as the lotus leaf, have a hierarchically structured surface roughness which is optimized for superhydrophobicity through natural selection. Here we present a molecular dynamics study of liquid droplets in contact with self-affine fractal surfaces. Our results indicate that the contact angle for nanodroplets depends strongly on the root-mean-square surface roughness amplitude but is nearly independent of the fractal dimension D(f) of the surface.

Boundary slip and wetting properties of interfaces: Correlation of the contact angle with the slip length

Correlations between contact angle, a measure of the wetting of surfaces, and slip length are developed using nonequilibrium molecular dynamics for a Lennard-Jones fluid in Couette flow between graphitelike hexagonal-lattice walls. The fluid-wall interaction is varied by modulating the interfacial energy parameter epsilonr=epsilonsfepsilonff and the size parameter sigmar=sigmasfsigmaff, (s=solid, f=fluid) to achieve hydrophobicity (solvophobicity) or hydrophilicity (solvophilicity). The effects of surface chemistry, as well as the effects of temperature and shear rate on the slip length are determined. The contact angle increases from 25 degrees to 147 degrees on highly hydrophobic surfaces (as epsilonr decreases from 0.5 to 0.1), as expected. The slip length is functionally dependent on the affinity strength parameters epsilonr and sigmar: increasing logarithmically with decreasing surface energy epsilonr (i.e., more hydrophobic), while decreasing with power law with decreasing size sigmar. The mechanism for the latter is different from the energetic case. While weak wall forces (small epsilonr) produce hydrophobicity, larger sigmar smoothes out the surface roughness. Both tend to increase the slip. The slip length grows rapidly with a high shear rate, as wall velocity increases three decades from 100 to 10(5) ms. We demonstrate that fluid-solid interfaces with low epsilonr and high sigmar should be chosen to increase slip and are prime candidates for drag reduction.