Anisotropic wetting behavior arising from superhydrophobic surfaces: parallel grooved structure

It has been found experimentally that superhydrophobic surfaces exhibit strong anisotropic wetting behavior. This study reports a simple but robust thermodynamic methodology to investigate the anisotropic superhydrophobic behavior for parallel grooved surfaces. Free energy and its barrier and the corresponding contact angle and its hysteresis for various orientations of the groove structure are calculated based on the proposed thermodynamic model. It is revealed that the strong anisotropy of equilibrium contact angle (ECA) and contact angle hysteresis (CAH) is shown in the noncomposite state but almost isotropic wetting properties are exhibited in the composite state. Furthermore, for the noncomposite state, decreasing groove width and spacing or increasing groove depth can amplify the anisotropy for ECA. Meanwhile, decreasing groove width and increasing depth can amplify the anisotropy for CAH, while varying groove spacing can barely influence CAH. For the composite state, however, the surface geometry hardly leads to the anisotropic behavior. In addition, using a fitting approximation, a simple quantitative correlation between wettability and orientation can be established well, which is consistent with the numerical calculations.     

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.     

Slip-stick wetting and large contact angle hysteresis on wrinkled surfaces

Wetting on a corrugated surface that is formed via wrinkling of a hard skin layer formed by UV oxidation (UVO) of a poly(dimethylsiloxane) (PDMS) slab is studied using advancing and receding water contact angle measurements. The amplitude of the wrinkled pattern can be tuned through the pre-strain of the PDMS prior to surface oxidation. These valleys and peaks in the surface topography lead to anisotropic wetting by water droplets. As the droplet advances, the fluid is free to move along the direction parallel to the wrinkles, but the droplet moving orthogonal to the wrinkles encounters energy barriers due to the topography and slip-stick behavior is observed. As the wrinkle amplitude increases, anisotropy in the sessile droplet increases between parallel and perpendicular directions. For the drops receding perpendicular to the wrinkles formed at high strains, the contact angle tends to decrease steadily towards zero as the drop volume decreases, which can result in apparent hysteresis in the contact angle of over 100°. The wrinkled surfaces can exhibit high sessile and advancing contact angles (>115°), but the receding angle in these cases is generally vanishing as the drop is removed. This effect results in micrometer sized drops remaining in the grooves for these highly wrinkled surfaces, while the flat analogous UVO-treated PDMS shows complete removal of all macroscopic water drops under similar conditions. These wetting characteristics should be considered if these wrinkled surfaces are to be utilized in or as microfluidic devices.     

Anisotropic drop morphologies on corrugated surfaces

The spreading of liquid drops on surfaces corrugated with micrometer-scale parallel grooves is studied both experimentally and numerically. Because of the surface patterning, the typical final drop shape is no longer spherical. The elongation direction can be either parallel or perpendicular to the direction of the grooves, depending on the initial drop conditions. We interpret this result as a consequence of both the anisotropy of the contact line movement over the surface and the difference in the motion of the advancing and receding contact lines. Parallel to the grooves, we find little hysteresis due to the surface patterning and that the average contact angle approximately conforms to Wenzel's law as long as the drop radius is much larger than the typical length scale of the grooves. Perpendicular to the grooves, the contact line can be pinned at the edges of the ridges, leading to large contact angle hysteresis.     

Wetting of nanogrooved polymer surfaces

Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie's equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel's equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.     

Directional self-cleaning superoleophobic surface

In this work, we report the creation of a grooved surface comprising 3 μm grooves (height ～4 μm) separated by 3 μm from each other on a silicon wafer by photolithography. The grooved surface was then modified chemically with a fluorosilane layer (FOTS). The surface property was studied by both static and dynamic contact angle measurements using water, hexadecane, and a polyethylene wax ink as the probing liquids. Results show that the grooved surface is both superhydrophobic and superoleophobic. Its observed contact angles agree well with the calculated Cassie-Baxter angles. More importantly, we are able to make a replica of the composite wax ink-air interface and study it by SEM. Microscopy results not only show that the droplet of the wax ink "sits" on air in the composite interface but also further reveal that the ink drop actually pins underneath the re-entrant structure in the side wall of the grooved structure. Contact angle measurement results indicate that wetting on the grooved surface is anisotropic. Although liquid drops are found to have lower static and advancing contact angles in the parallel direction, the drops are found to be more mobile, showing smaller hysteresis and lower sliding angles (as compared to the FOTS wafer surface and a comparable 3-μm-diameter pillar array FOTS surface). The enhanced mobility is attributable to the lowering of the resistance against an advancing liquid because 50% of the advancing area is made of a solid strip where the liquid likes to wet. This also implies that the contact line for advancing is no longer smooth but rather is ragged, having the solid strip area leading the wetting and the air strip area trailing behind. This interpretation is supported by imaging the geometry of the contact lines using molten ink drops recovered from the sliding angle experiments in both the parallel and orthogonal directions. Because the grooved surface is mechanically stronger against mechanical abrasion, the self-cleaning effect exhibited in the parallel direction suggests that groove texturing is a viable approach to create mechanically robust, self-cleaning, superoleophobic surfaces.     

Macroscopic-wetting anisotropy on the line-patterned surface of fluoroalkylsilane monolayers

Micropatterned fluoroalkylsilane monolayer surfaces with liquidphilic/liquidphobic area (line width 1-20 microm) were prepared with few defects by vacuum ultraviolet (VUV) photolithography. The anisotropic wetting of a macroscopic droplet with a 0.5-5 mm diameter on the micropatterned surfaces was investigated. The strong anisotropy of the contact angle and the sliding angle and droplet distortion for fluoroalkylsilane/silanol patterned surfaces was attributed to the difference in the energy barrier of wetting between parallel and orthogonal lines. The wetting anisotropy decreased with decreases in the liquidphilic area. Fluoroalkylsilane/alkylsilane patterned surfaces with small differences in the surface free energies of the components showed anisotropic wetting only for the low-surface-tension liquids.     

On the role of energy barriers in determining contact angle hysteresis

The thermodynamic model of contact angles on rough, heterogeneous surfaces developed by Long et al. [J. Long, M.N. Hyder, R.Y.M. Huang and P. Chen, Adv. Colloid Interface Sci. 118 (2005) 173] was employed to study the role of energy barriers in determining contact angle hysteresis. Major energy barriers corresponding to metastable states and minor energy barriers corresponding to secondary metastable states were defined. Distributions of major and/or minor energy barriers as a function of apparent contact angle for various surfaces were obtained. The reproducibility of contact angle measurement, the effect of vibrational energy on contact angle hysteresis and the "stick-slip" phenomenon were discussed. Quantitative relations between contact angles and vibrational energy were obtained. It was found that receding contact angles are normally poorly reproducible for hydrophilic surfaces, but for extremely hydrophobic surfaces, advancing contact angles may have a poor reproducibility. When the vibrational energy available to a system increases, the measured advancing contact angle will decrease while the receding angle will increase until both reach a common value: the system equilibrium angle. This finding not only agrees well with the experimental observations in system equilibrium contact angle measurements, but also lays a theoretical foundation for such measurements. A small vibrational energy may result in a "stick-slip" phenomenon.     

Methodology for calculating the volume of condensate droplets on topographically modified, microgrooved surfaces

Liquid droplets on micropatterned surfaces consisting of parallel grooves tens of micrometers in width and depth are considered, and a method for calculating the droplet volume on these surfaces is presented. This model, which utilizes the elongated and parallel-sided nature of droplets condensed on these microgrooved surfaces, requires inputs from two droplet images at ? = 0° and ? = 90°--namely, the droplet major axis, minor axis, height, and two contact angles. In this method, a circular cross-sectional area is extruded the length of the droplet where the chord of the extruded circle is fixed by the width of the droplet. The maximum apparent contact angle is assumed to occur along the side of the droplet because of the surface energy barrier to wetting imposed by the grooves--a behavior that was observed experimentally. When applied to water droplets condensed onto a microgrooved aluminum surface, this method was shown to calculate the actual droplet volume to within 10% for 88% of the droplets analyzed. This method is useful for estimating the volume of retained droplets on topographically modified, anisotropic surfaces where both heat and mass transfer occur and the surface microchannels are aligned parallel to gravity to assist in condensate drainage.     

Wetting on axially-patterned heterogeneous surfaces

Contact angle variability, leading to errors in interpretation, arises from various sources. Contact angle hysteresis (history-dependent wetting) and contact angle multiplicity (corrugation of three-phase contact line) are irrespectively the most frequent causes of this uncertainty. Secondary effects also derived from the distribution of chemical defects on solid surfaces, and so due to the existence of boundaries, are the known "stick/jump-slip" phenomena. Currently, the underlying mechanisms in contact angle hysteresis and their connection to "stick/jump-slip" effects and the prediction of thermodynamic contact angle are not fully understood. In this study, axial models of smooth heterogeneous surface were chosen in order to mitigate contact angle multiplicity. For each axial pattern, advancing, receding and equilibrium contact angles were predicted from the local minima location of the system free energy. A heuristic model, based on the local Young equation for spherical drops on patch-wise axial patterns, was fruitfully tested from the results of free-energy minimization. Despite the very simplistic surface model chosen in this study, it allowed clarifying concepts usually misleading in wetting phenomena.     

Effects of geometrical characteristics of surface roughness on droplet wetting

Surface roughness is known to alter the wettability on a solid substrate. In general, either Wenzel or Cassie-Baxter theory is adopted to describe the apparent contact angle. Following the minimum free energy pathway associated with the imbibition process, we have derived a generalized expression for the apparent contact angle on a textured surface and the liquid-gas contact area within the groove that plays a key role. Depending on the geometrical characteristics of the grooves, the surface wetting falls into three regimes: (i) single stable state which is either Wenzel (completely wetted roughness) or Cassie-Baxter (completely nonwetted roughness) state, (ii) two stable states (Wenzel and Cassie-Baxter) separated by an energy barrier, and (iii) single stable state with partially wetted roughness. The sufficient condition for each regime is derived and several groove geometries are given to show the free energy path. Alteration in the geometric parameters may lead to the wetting crossover. We also show that the Cassie-Baxter can occur at a hydrophilic surface for particular pore shapes.     

A thermodynamic approach for determining the contact angle hysteresis for superhydrophobic surfaces

Contact angle hysteresis (CAH) is critical to superhydrophobicity of a surface. This study proposes a free energy thermodynamic analysis (of a 2-D model surface) that significantly simplifies calculations of free energy barrier associated with CAH phenomena. A microtextured surface with pillar structure, typical of one used in experimental studies, is used as an example. We demonstrate that the predicted CAH and equilibrium contact angles are consistent with experimental observations and predictions of Wenzel's and Cassie's equations, respectively. We also establish a criterion for transition between noncomposite and composite wetting states. The results and methodology presented can potentially be used for designing superhydrophobic surfaces.     

Control over wettability of polyethylene glycol surfaces using capillary lithography

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

Constitutive modeling of contact angle hysteresis

We introduce a phase field model of wetting of surfaces by sessile drops. The theory uses a two-dimensional non-conserved phase field variable to parametrize the Gibbs free energy of the three-dimensional system. Contact line tension and contact angle hysteresis arise from the gradient term in the free energy and the kinetic coefficient respectively. A significant advantage of this approach is in the constitutive specification of hysteresis. The advancing and receding angles of a surface, the liquid-vapor interfacial energy and three-phase line tension are the only required constitutive inputs to the model. We first simulate hysteresis on a smooth chemically homogeneous surface using this theory. Next we show that it is possible to study heterogeneous surfaces whose component surfaces are themselves hysteretic. We use this theory to examine the wetting of a surface containing a circular heterogeneous island. The contact angle for this case is found to be determined solely by the material properties at the contact line in accord with recent experimental data.     

Alignment mechanism of a nematic liquid crystal on a pre-rubbed polyimide film with laser-induced periodic surface structure

A periodic surface structure was prepared on a pre-rubbed polyimide (PI) film surface with a pulsed UV laser polarized perpendicular to the rubbing direction. The experimental results demonstrate that the rubbing-induced molecular anisotropic orientation was relaxed by the pulsed laser irradiation, and the laser induced molecular orientation was perpendicular to the line of the laser-induced periodic structure. The dichroism of the anisotropy of molecular orientation increased with the increase of laser energy. Since the direction of the laser-induced molecular anisotropy was perpendicular to the surface groove direction of the pre-rubbed PI surface, the effects of surface microgroove and anisotropic molecular orientation of the PI chain on liquid crystal (LC) alignment can be distinguished from each other. LC alignment was investigated by evaluating the anchoring energy of the PI surface, which was calculated according to Berreman's theory using the twist angle of the LC in the cells. The experimental results demonstrate that the exact alignment direction of the LC molecules is determined by the relative strength of both factors.     

On some relations between advancing, receding and Young's contact angles

Problems of experimental determination and theoretical verification of equilibrium contact angles are discussed basing on the literature data. A relationship between the advancing and receding contact angles versus the equilibrium contact angle is described and then verified using the literature contact angles determined on paraffin wax and polypropylene. Using the proposed relationship and experimentally determined equilibrium contact angles, obtained by plotting the advancing and receding contact angles versus the contact angle hysteresis or by applying vibration of the system liquid drop/solid surface, it is found that the same value of the surface free energy for paraffin wax is calculated from the contact angles of water and ethylene glycol. However, in the case of polypropylene some inconsistency appears between the equilibrium contact angles of the probe liquid used and the calculated surface free energy. More experimental data of the equilibrium contact angle are needed to verify further the relationship.     

Droplets wetting on filament rails: Surface energy and morphology transition

The morphology of liquid droplets wetting on filaments depends on the filament configuration, droplet volume, and contact angle. A stable morphology is the one that minimizes the potential energy of the droplet–filament system, while morphology transition may happen when an intermediate state exists which corresponds to a higher potential energy. This paper aims to explore such morphology transition of droplet wetting on filament rails made of two parallel identical microfilaments. Detailed numerical simulations were performed to extract the surface energy of the droplet–filament system at varying filament spacings, droplet volumes, and contact angles. Critical conditions of the morphology transition between two symmetrical wetting morphologies (i.e., liquid droplet bridge and barrel-shaped droplet) were determined. A family of characteristic curves in terms of the dimensionless droplet volume vs the filament spacing at varying contact angles was obtained, which can be used as a universal law to govern the morphology transition for such droplet–filament rail systems. The results and concepts presented in this work can be extended to broad wetting systems and utilized for the analysis and design of microfluidic devices and testers based on droplet–filament systems.     

Alignment mechanism of a nematic liquid crystal on a pre-rubbed polyimide film with laser-induced periodic surface structure

A periodic surface structure was prepared on a pre-rubbed polyimide (PI) film surface with a pulsed UV laser polarized perpendicular to the rubbing direction. The experimental results demonstrate that the rubbing-induced molecular anisotropic orientation was relaxed by the pulsed laser irradiation, and the laser induced molecular orientation was perpendicular to the line of the laser-induced periodic structure. The dichroism of the anisotropy of molecular orientation increased with the increase of laser energy. Since the direction of the laser-induced molecular anisotropy was perpendicular to the surface groove direction of the pre-rubbed PI surface, the effects of surface microgroove and anisotropic molecular orientation of the PI chain on liquid crystal (LC) alignment can be distinguished from each other. LC alignment was investigated by evaluating the anchoring energy of the PI surface, which was calculated according to Berreman's theory using the twist angle of the LC in the cells. The experimental results demonstrate that the exact alignment direction of the LC molecules is determined by the relative strength of both factors.     

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.     

Theoretical contact angles on a nano-heterogeneous surface composed of parallel apolar and polar strips

Neumann-Good's parallel strip model (J. Colloid Interface Sci. 1972, 38, 341) was used to analyze the contact angle hysteresis for a liquid on a heterogeneous surface composed of alternatively aligned horizontal apolar (theta = 70 degrees ) and polar (theta = 0 degree ) strips. The critical size of the strip width, below which the contact angle hysteresis disappears, was determined on the basis of the analysis of the activation energy for wetting to be from 6 to 12 nm. This calculated value of the critical strip size is 1 order of magnitude smaller than that of 0.1 microm, which has been commonly considered as the limit of heterogeneity size causing the appearance of the contact angle hysteresis.