Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.     

Drops down the hill: theoretical study of limiting contact angles and the hysteresis range on a tilted plate

The limiting inclination angle (slip angle), for which a two-dimensional water drop may be at equilibrium on a chemically heterogeneous surface, is exactly calculated for a variety of cases. The main conclusion is that, in the cases studied, the contact angles at the upper and lower contact line do not always simultaneously equal the receding and advancing contact angles, respectively. On a hydrophobic surface, the lowest contact angle (at the upper contact line) tends to be approximately equal to the receding contact angle, while the highest contact angle (at the lower contact line) may be much lower than the advancing contact angle. For hydrophilic surfaces, the opposite is true. These conclusions imply that the hysteresis range cannot in general be measured by analyzing the shape of a drop on an inclined plane. Also, the limiting inclination angle cannot in general be calculated from the classical equation based only on the advancing and receding contact angles.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.     

Dynamic behavior of polymer surface and the time dependence of contact angle

The increased attention has been focused on the re-searches of soft materials proposed by Pierre-Gilles de Gennes, a Nobel Prize Laureate in Physics. A special issue of “Science” on soft surfaces was published in 2002 to review specific surface properti…     

Creation of low hysteresis superhydrophobic paper by deposition of hydrophilic diamond-like carbon films

The creation of low hysteresis superhydrophobic paper is reported using a combination of oxygen plasma etching and plasma deposition of an 80 nm non-fluorinated, hydrophilic diamond-like carbon (DLC) coating. The DLC has an equilibrium (flat surface) contact angle (θ _e ) of 68.2° ± 1.5°, which is well below the 90° contact angle that is typically believed to be a prerequisite for superhydrophobicity. Coating of paper substrates with the DLC film yields an advancing contact angle of 124.3° ± 4.1°, but the surface remains highly adhesive, with a receding contact angle <10°. After 60 min of plasma etching and DLC coating, a low hysteresis, superhydrophobic surface is formed with an advancing contact angle of 162.0° ± 6.3° and hysteresis of 8.7° ± 1.9°. To understand the increase in contact angle and decrease in hysteresis, atomic force microscopy and optical profilometry studies were performed. The data demonstrates that while little additional nanoscale roughness is imparted beyond the first 5 min of etching, the roughness at the microscale continually increases. The hierarchical structure provides the appropriate roughness to create low hysteresis superhydrophobic paper from a hydrophilic coating.     

Ratchetlike slip angle anisotropy on printed superhydrophobic surfaces

The fabrication and properties of superhydrophobic surfaces that exhibit ratchet-like anisotropic slip angle behavior is described. The surface is composed of arrays of poly(dimethylsiloxane) (PDMS) posts fabricated by a type of 3D printing. By controlling the dispense parameters, regular arrays of asymmetric posts were deposited such that the slope of the posts was varied from 0 to 50 relative to the surface normal. Advancing and receding contact angles as well as slip angles were measured as a function of the post slope and droplet volume. Ratchetlike slip angle anisotropy was observed on surfaces composed of sloped features. The maximum slip angle difference (for a 180° tilt angle variation) was 32° for 20 μL droplets on surfaces with posts fabricated with a slope of 50°. This slip angle anisotropy is attributed to an increase in the triple contact line (TCL) length as the droplet is tilted in a direction against the post slope whereas the TCL decreases continuously when the drop travels in a direction parallel to the post slope. The increasing length of the TCL creates an increased energy barrier that accounts for the higher slip angles in this direction.     

Line energy and the relation between advancing, receding, and young contact angles

The line energy associated with the triple phase contact line is a function of local surface defects (chemical and topographical); however, it can still be calculated from the advancing and receding contact angles to which those defects give rise. In this study an expression for the line energy associated with the triple phase contact line is developed. The expression relates the line energy to the drop volume, the interfacial energies, and the actual contact angle (be it advancing, receding, or in between). From the expression we can back calculate the equilibrium Young contact angle, theta0, as a function of the maximal advancing, thetaA, and minimal receding, thetaR, contact angles. To keep a certain maximal hysteresis between advancing and receding angles, different line energies are required depending on the three interfacial energies and the drop's volume V. We learn from the obtained expressions that the hysteresis is determined by some dimensionless parameter, K, which is some normalized line energy. The value of K required to keep a constant hysteresis (thetaA-thetaR) rises to infinity as we get closer to theta0 = 90 degrees.     

Thermoresponsive poly(N-isopropylacrylamide) copolymers: contact angles and surface energies of polymer films

Surface properties of poly(N-isopropylacrylamide) (PNIPAM) copolymer films were studied by contact angle measurements and optical and atomic force microscopy. We prepared a series of copolymers of N-isopropylacrylamide with N-tert-butylacrylamide (NtBA) in order of increasing hydrophobicity. The measurements of the advancing contact angle of water at 37 degrees C were hampered by the observation of a distinct stick/slip pattern on all polymers in the series with the exception of poly(NtBA) (PNtBA). We attributed this behavior to the film deformation by the vertical component of liquid surface tension leading to the pinning of the moving contact line. This was confirmed by the observation of a ridge formed at the pinned contact line by optical microscopy. However, meaningful contact (without the stick/slip pattern and with a time-independent advancing contact angle) angles for this thermoresponsive polymer series could be obtained with carefully selected organic liquids. We used the Li and Neumann equation of state to calculate the surface energy and contact angles of water for all polymers in the series of copolymers and van Oss, Chaudhury, and Good (vOCG) acid-base theory for PNtBA. The surface energies of the thermoresponsive polymers were in the range of 38.9 mJ/m2 (PNIPAM) to 31 mJ/m2 (PNtBA) from the equation of state approach. The surface energy of PNtBA calculated using vOCG theory was 29.0 mJ/m2. The calculated contact angle for PNIPAM (74.5 +/- 0.2 degrees ) is compared with previously reported contact angles obtained for PNIPAM-modified surfaces.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Study of the advancing and receding contact angles: liquid sorption as a cause of contact angle hysteresis

Two types of experiments were used to study the behavior of both advancing and receding contact angles, namely the dynamic one-cycle contact angle (DOCA) and the dynamic cycling contact angle (DCCA) experiments. For the preliminary study, DOCA measurements of different liquids on different solids were performed using an automated axisymmetric drop shape analysis-profile (ADSA-P). From these experimental results, four patterns of receding contact angle were observed: (1) time-dependent receding contact angle; (2) constant receding contact angle; (3) 'stick/slip'; (4) no receding contact angle. For the purpose of illustration, results from four different solid surfaces are shown. These solids are: FC-732-coated surface; poly(methyl methacrylate/n-butyl methacrylate) [P(MMA/nBMA)]; poly(lactic acid) (DL-PLA); and poly(lactic/glycolic acid) 50/50 (DL-PLGA 50/50). Since most of the surfaces in our studies exhibit time dependence in the receding contact angle, a more extended study was conducted using only FC-732-coated surfaces to better understand the possible causes of decreasing receding contact angle and contact angle hysteresis. Contact angle measurements of 21 liquids from two homologous series (i.e. n-alkanes and 1-alcohols) and octamethylcyclotetrasiloxane (OCMTS) on FC-732-coated surfaces were performed. It is apparent that the contact angle hysteresis decreases with the chain length of the liquid. It was found that the receding contact angle equals the advancing angle when the alkane molecules are infinitely large. These results strongly suggest that the chain length and size of the liquid molecule could contribute to contact angle hysteresis phenomena. Furthermore, DCCA measurements of six liquids from the two homologous series on FC-732-coated surfaces were performed. With these experimental results, one can construe that the time dependence of contact angle hysteresis on relatively smooth and homogeneous surfaces is mainly caused by liquid retention/sorption. The results also suggested that the contact angle hysteresis will eventually approach a steady state, where the rate of liquid retention-evaporation or sorption process would balance out each other. If the existence of contact angle hysteresis can be attributed to liquid sorption/retention, one should only use the advancing contact angles (measured on a dry surface) in conjunction with Young's equation for surface energetic calculations.     

Effects of plasma treatments for improving extreme wettability behavior of cotton fabrics

A simple, environmentally benign and energy efficient process for fabricating single faced superhydrophilic/hydrophobic cotton fabrics by controlling surface texture and chemistry at the nano/microscale is reported here. Stable ultra-hydrophobic surfaces with advancing and receding water droplet contact angles in excess of 146° as well as extreme superhydrophilic surfaces are obtained. Hydrophobic water-repellent cotton fabrics were obtained following plasma treatment through diamond-like carbon (DLC) coating by plasma enhanced chemical vapour deposition. The influence of changing different precursor’s plasma pre-treatments such as H₂, Ar or O₂ on the properties of DLC coatings is also evaluated using atomic force microscopy, X-ray photoelectron spectroscopy, attenuated total reflection Fourier transform infrared spectroscopy, and analysed in terms of contact angle measurements. Because of the DLC coating, the coated fabric showed to endure its superhydrophobic character even after 12 months.     

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.     

Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces

A simulation study of liquid drops on inclined surfaces is performed in order to understand the evolution of drop shapes, contact angles, and retention forces with the tilt angle. The simulations are made by means of a method recently developed for dealing with contact angle hysteresis in the public-domain Surface Evolver software. The results of our simulations are highly dependent on the initial contact angle of the drop. For a drop with an initial contact angle equal to the advancing angle, we obtain results similar to those of experiments in which a drop is placed on a horizontal surface that is slowly tilted. For drops with an initial contact angle equal to the mean between the advancing and the receding contact angles, we recover previous results of finite element studies of drops on inclined surfaces. Comparison with experimental results for molten Sn-Ag-Cu on a tilted Cu substrate shows excellent agreement.     

Bioinspired synthesis of superhydrophobic coatings

A superhydrophobic material prepared by precipitating calcium phosphate on TiO2 films under in vitro conditions is described. Crystalline calcium phosphate is very porous with octacalcium phosphate as the main phase. The films are made hydrophobic by the surface grafting of a perfluorophosphate surfactant (Zonyl FSE). The as-prepared coatings were strongly hydrophobic, with advancing contact angles exceeding 165 degrees and receding angles exceeding 150 degrees . The formation of the calcium phosphate layer is self-organizing, and the coating is easily functionalized. The material was characterized with dynamic contact angle measurements, SEM, XRD, and XPS. The strong water repellency is explained by the open porous morphology of the calcium phosphate coating together with the successful attachment of the hydrophobic function.     

Characterization of super liquid-repellent surfaces

Characterization of the wetting properties is a prerequisite for a fundamental understanding and the targeted development of superhydrophobic and superamphiphobic layers. To fabricate super liquid-repellent layers, two requirements need to be met: The surfaces have to be of low energy and their nano- and microstructure needs to be designed in a way that leads to the entrapment of air. The challenge is to design and produce suitable nano- and microstructures to control wetting. Here we describe important methods to quantify wetting properties of super liquid-repellent layers. These properties include the apparent advancing and receding contact angles, the roll-off angle, tensile and lateral adhesion, the impalement pressure, and the observation of drop impact. The most important one is the apparent receding contact angle because it also limits lateral adhesion. The link of these properties to the nano- and microscopic structure of the layer is discussed. Limits, problems, and future challenges are pointed out.     

Thermo-responsive superhydrophobic paper using nanostructured cellulose stearoyl ester

Hydrophilic paper was rendered with hydrophobic and superhydrophobic property after the treatment with solutions and nanoparticles of cellulose stearoyl ester (CSE), respectively. Cellulose stearoyl ester with a degree of substitution of 2.99 was synthesized from cellulose using stearoyl chloride. By dip-coating paper in CSE solution of at least 3 mg/ml in toluene, paper became hydrophobic with stable water contact angles of more than 120°. After further spray-coating using CSE nanoparticles that were prepared from CSE solution via nanoprecipitation, paper surface became superhydrophobic with water contact angles of larger than 150°. These superhydrophobic surfaces also exhibited self-cleaning character. Furthermore, the superhydrophobic paper surfaces showed a temperature-responsive character and could be turned hydrophobic after a heat-treatment at 70 °C for 5 min.     

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.     

Ultralow hysteresis superhydrophobic surfaces by excimer laser modification of SU-8

We present a new and simple method to produce superhydrophobic surfaces with ultralow hysteresis. The method involves surface modification of SU-8 using an excimer laser treatment. The modified surface is coated with a hydrophobic plasma-polymerized hexafluoropropene layer. The advancing and receding water contact angles were measured to be approximately 165 degrees . The achieved water contact angle hysteresis was below the measurement limit. This low hysteresis can be ascribed to nanoscale debris generated during the excimer laser process.     

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.     

Contact angle hysteresis of microbead suspensions

Microbead suspensions are often used in microfluidic devices for transporting biomolecules. An experimental investigation on the wettability of microbead suspension is presented in this study. The variation in the surface tension and the equilibrium contact angle with the change in the volume fraction of the microbead is presented here. The surface tension of the microbead suspension is measured with the pendant drop technique, whereas the dynamic contact angle measurements, i.e., advancing and receding contact angles, are measured with the sessile drop technique. An equilibrium contact angle of a suspension with particular volume fraction is determined by computing an average over the measured advancing and receding contact angles. It is observed that the surface tension and the equilibrium contact angle determined from advancing and receding contact angles vary with the magnitude of the microbeads volume fraction in the suspension. A decrease in the surface tension with an increase in the volume fraction of the microbead suspension is observed. The advancement and the recession in contact line for dynamic contact angle measurements are achieved with the motorized dosing mechanism. For microbead suspensions, the advancement of the contact line is faster as compared to the recession of the contact line for the same flow rate. The presence of microbeads assists in the advancement and the recession of the contact line of the suspension. A decrease in the equilibrium contact angles with an increase in the microbead suspension volume fraction is observed. Inclusion of microbeads in the suspension increases the wetting capability for the considered combination of the microbead suspension and substrate. Finally, empirical correlations for the surface tension and the contact angle of the suspension as a function of microbead volume fraction are proposed. Such correlations can readily be used to develop mechanistic models for the capillary transport of microbead suspensions related to LOC applications.