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.     

Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

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…     

Water contact angles and hysteresis of polyamide surfaces

The wetting behavior of a series of aliphatic polyamides (PAs) has been examined. PAs with varying amide content and polyethylene (PE) were molded against glass to produce surfaces with similar roughness. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while hysteresis increased. Hysteresis arose primarily from molecular interactions between the contact liquid and the solid substrates, rather than moisture absorption, variations in crystallinity, surface deformation, roughness, reorientation of amide groups, or surface contamination. Free energies of hysteresis were calculated from contact angles. For PE, which is composed entirely of nonpolar methylene groups, free energies were equivalent to the strength of dispersive van der Waals bonds. For PAs, free energies corresponded to fractional contributions from the dispersive methylene groups and polar amide groups.     

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

Contact angles and their hysteresis as a measure of liquid-solid adhesion

The wetting behavior of a series of aliphatic polyamides was examined. Polyamides and polyethylene were molded against glass to produce smooth surfaces. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while contact angle hysteresis increased. Wetting free energies calculated from contact angles were equal to those from dewetting, suggesting that contact angle hysteresis did not arise from surface anomalies, but from hydrogen bonding between water and the amide groups in the polyamide surfaces.     

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.     

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.     

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.     

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.     

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.     

Roughness assessment and wetting behavior of fluorocarbon surfaces

The wetting behavior of fluorocarbon materials has been studied with the aim of assessing the influence of the surface chemical composition and surface roughness on the water advancing and receding contact angles. Diamond like carbon and two fluorocarbon materials with different fluorine content have been prepared by plasma enhanced chemical vapor deposition and characterized by X-ray photoemission, Raman and FT-IR spectroscopies. Very rough surfaces have been obtained by deposition of thin films of these materials on polymer substrates previously subjected to plasma etching to increase their roughness. A direct correlation has been found between roughness and water contact angles while a superhydrophobic behavior (i.e., water contact angles higher than 150° and relatively low adhesion energy) was found for the films with the highest fluorine content deposited on very rough substrates. A critical evaluation of the methods currently used to assess the roughness of these surfaces by atomic force microscopy (AFM) has evidenced that calculated RMS roughness values and actual surface areas are quite dependent on both the scale of observation and image resolution. A critical discussion is carried out about the application of the Wenzel model to account for the wetting behavior of this type of surfaces.     

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.     

Microspreading studies on rough surfaces by scanning electron microscopy

The use of scanning electron microscopy for direct observation of the effects of surface roughness on the spreading of liquids is described, making it possible to view moving liquid drops at distances less than 1 μm from the advancing contact line. Various surfaces were examined including several with simple forms of roughness which can assist in explaining the behavior of more complex surfaces. Spreading is shown to be highly dependent on the orientation and texture of the roughness; in particular, the presence of sharp edges of step height 0.05 μm are shown to influence spreading significantly. These observations reinforce our previously stated doubts of the significance of conventionally measured macroscopic contact angles.     

Liquid drops on vertical and inclined surfaces; I. An experimental study of drop geometry

Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces. Two liquids and eight surfaces have been used to study contact angles, contact lines, profiles, and volumes of drops of different sizes for a range of surface conditions. The results show the contact-angle variation along the circumference of a drop to be best fit by a third-degree polynomial in the azimuthal angle. This contact-angle function is expressed in terms of the maximum and minimum contact angles of the drop, which are determined for various conditions. The maximum contact angle, thetamax, is approximately equal to the advancing contact angle, thetaA, of the liquid on the surface. As the Bond number, Bo, increases from 0 to a maximum, the minimum contact angle, thetamin, decreases almost linearly from the advancing to the receding angle. A general relation is found between thetamin/thetaA and Bo for different liquid-surface combinations. The drop contour can be described by an ellipse, with the aspect ratio increasing with Bo. These experimental results are valuable in modeling drop shape, as presented in Part II of this work.     

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.     

The wetting behavior of grafted hydrophilic acrylic monomers

The wetting behavior of vapor phase photografted hydrophilic acrylic monomers was evaluated by the three most commonly employed techniques, i.e., the captive bubble, the sessile drop, and the Wilhelmy plate technique. The measured contact angles and the overall wetting behavior were discussed in light of the non-ideal nature of these surfaces.It was found that the peculiar nature of hydrophilic grafted surfaces is carefully reflected in the experimentally measurable contact angles. While in the case of the captive bubble the hydrophilic and rough nature of these coatings prevent the bubble-surface contact, in the case of the sessile drop the measured contact angles follow the behavior predicted by contact angle hysteresis theories. Wilhelmy plate measurements, performed as sequential scanning loops, show velocity-dependent effects which are linked to the composition, morphology and mobility of the grafted surfaces.     

Contact angles of liquid drops on super hydrophobic surfaces: understanding the role of flattening of drops by gravity

Measurement of contact angles on super hydrophobic surfaces by conventional methods can produce ambiguous results. Experimental difficulties in constructing tangent lines, gravitational distortion or erroneous assumptions regarding the extent of spreading can lead to underestimation of contact angles. Three models were used to estimate drop shape and perceived contact angles on completely nonwetting super hydrophobic surfaces. One of the models employed the classic numerical solutions from Bashforth and Adams. Additionally, two approximate models were derived as part of this work. All three showed significant distortion of microliter-sized drops and similar trends in perceived contact angles. Liquid drops of several microliters are traditionally used in sessile contact angle measurements. Drops of this size are expected to and indeed undergo significant flattening on super hydrophobic surfaces, even if the wetting interactions are minimal. The distortion is more pronounced if the liquid has a lesser surface tension or greater density. For surfaces that are completely nonwetting, underestimation of contact angles can be tens of degrees. Our modeling efforts suggest that accurate contact angle measurements on super hydrophobic surfaces would require very small sessile drops, on the order of hundreds of picoliters.     

Empirical study and prediction of liquids retention on structured polymer surfaces

Liquids' contact angle hysteresis and critical retention volumes on five commonly used plastics with surface structures were studied. The chevron‐like groove structures, which are orthogonally arranged, make the liquid–solid contact line elongated while the droplet found staying in the Wenzel state. Various dimensions of surface structures were represented by contact length ratio σ. Advancing and receding contact angles of liquids on polymer surfaces with various conditions were reported. Reduced hysteresis H, which links between advancing and receding contact angles, was also studied and found to extend its availability on structured surfaces. The research found that surface structures have linear effects on liquids' advancing contact angles in the range of σ = 1.0 to 1.42. Linear regression analysis was hence proposed to predict advancing contact angles, and the results indicate that approximate 80% of data points have less than 6% error. An empirical model, which adopts liquid–solid surface tension as the source of liquids' retention force, was proposed to estimate liquids' critical retention volumes on inclined surfaces. The proposed model found good agreements with existing experiment data and demonstrated its superiority over previous ones. The present model provides an approach to predict liquids' storage/repellency on structured surfaces when the advancing contact angles are predictable. Copyright © 2016 John Wiley & Sons, Ltd.     

Retention forces and contact angles for critical liquid drops on non-horizontal surfaces

Retention forces and drop parameters are investigated for drops on the verge of sliding on vertical and inclined surfaces. Using earlier observations of drop geometry, the retentive-force factor relating surface-tension forces to contact-angle hysteresis is reliably determined. The retention force for a drop is found to be insignificantly affected by the aspect ratio of its contour. The maximum size of a drop is predicted with good accuracy, based on the two-circle method for approximating shapes of drops. The Bond number of a critical drop is found to be constant for a given surface and liquid. A general relation is proposed between the characteristic advancing and receding contact angles. The relation is supported by a large set of contact-angle data. In the absence of theta R data, the relation allows estimating the receding contact angle and the critical drop size, using only the advancing angle.