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.     

Surface free energy and wettability of silyl layers on silicon determined from contact angle hysteresis

Using the literature data of the advancing and receding contact angles for water, diiodomethane and hexadecane measured on various hydrophobic silyl layers (mostly monolayers) produced on silicon wafers the apparent surface free energies gamma(s)(tot) were calculated by applying new model of the contact angle hysteresis interpretation. It was found that, for the same silyl layer, the calculated gamma(s)(tot) values to some degree depended on the probe liquid used. Therefore, thus calculated the surface free energies should be considered as apparent ones. Moreover, also the values of the dispersion component gamma(s)(d) of these layers depend on the probe liquid used, but to a less degree. This must be due to the strength of the force field originating from the probe liquid and the spacing between the interacting molecules. The relationships between gamma(s)(tot) and gamma(s)(d) are discussed on the basis of the equations derived. It may be postulated that applying proposed model of the contact angle hysteresis and calculating the apparent total surface free energies and the dispersion contributions better insight into wetting properties of the silyled silicon surface can be achieved.     

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.     

Estimation of surface free energies and hamaker constants for fibrous solids by wetting force measurements

Wetting force at three-phase line was measured by the Wilhelmy technique using fibrous solids/liquid/liquid systems. Advancing and receding contact angles were calculated from the wetting forces during fiber immersion and emersion. The obtained results showed that contact angle hysteresis was due to the heterogeneity of the fiber surfaces. The dispersive and polar components of surface free energies of the fibers were determined from the advancing and receding contact angles, respectively. The Hamaker constants of the fibers were estimated from the dispersive components of their surface free energies.     

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.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

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.     

Zeta potential and surface free energy changes of solid-supported phospholipid (DPPC) layers caused by the enzyme phospholipase A2 (PLA2)

Stability and wetting properties changes of systems formed of phospholipid DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) layers covering silica particles or glass slides due to the phospholipase A₂ (PLA₂) action were determined by zeta potential measurements and the surface free energy evaluation, respectively. The comparison of the zeta potential and surface free energy, which was evaluated from advancing and receding contact angles via applying models of interfacial interactions, i.e. van Oss et al. (LWAB) and contact angle hysteresis (CAH), was found to be helpful for better understanding the mechanism of PLA₂ action on the lipid layers, what is discussed in the paper.     

Two-dimensional fluidics based on differential lyophobicity and gravity

We have prepared planar fluidics devices using binary chemical patterns consisting of hydrophobic "roads" on which water droplets slide easily and more hydrophobic "curbs" that direct droplet motion. Contact angle and contact angle hysteresis both control the motion of liquid droplets on surfaces. The difference between the advancing contact angles of the two regions prevents the liquid from crossing the interface between them. The low hysteresis of the roads allows facile movement. Gravity (slight tilting of samples) forces droplets to move effortlessly in defined pathways even though the difference in contact angles is not large and both regions are hydrophobic.     

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.     

Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface

Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference. The wetting characteristics on the patterned surfaces were studied by contact angle measurements. Macroscopic distortion of water drops was found on such small-scale surface structures, and the contact angles measured from the direction parallel to the grooves were larger than those measured from the perpendicular direction. A thermodynamic model was developed to calculate the change in the surface free energy as a function of the instantaneous contact angle when the three-phase contact line (TPCL) moves along the two orthogonal directions. It was found that the fluctuations, i.e., energy barriers, on the energy versus contact angle curves are crucial to the analysis of wetting anisotropy and contact angle hysteresis. The calculated advancing and receding contact angles from the energy versus contact angle curves were in good agreement with those measured experimentally. Furthermore, with the groove depth increasing, both the degree of wetting anisotropy and the contact angle hysteresis perpendicular to the grooves increased as a result of the increase in the energy barrier. The theoretical critical value of the groove depth, above which the anisotropic wetting appears, was determined to be 16 nm for the grooved surface with a wavelength of 396 nm. On the other hand, the effect of the groove wavelength on the contact angle hysteresis perpendicular to the grooves was also interpreted on the basis of the thermodynamic model. That is, with the wavelength decreasing, the contact angle hysteresis increased due to the increase in the number of energy barriers. These results may provide theoretical evidence for the design and application of anisotropic wetting surface.     

Contact angle measurements with liquids consisting of bulky molecules

Well-measured contact angles with different solid-liquid systems fall approximately on smooth patterns when plotted versus liquid surface tension. However, there are deviations of 1 degrees -3 degrees , which are outside the error limits. It is the purpose of this paper to elucidate the reasons for such deviations. Two types of liquids were selected for advancing contact angle measurements on Teflon AF 1600 coated surfaces: a series of n-alkanes ranging from n-hexane to n-hexadecane and five liquids consisting of bulky molecules, octamethylcyclotetrasiloxane (OMCTS), methyl salicylate, tetralin, cis-decalin, and octamethyltrisiloxane (OMTS). It was found that contact angles of the liquids with bulky molecules fall on a perfectly smooth curve corresponding to a solid surface tension of 13.64 +/- 0.1 mJ/m2. However, contact angles of n-alkanes deviated from this curve by up to 3 degrees in a complicated fashion. The observed trend suggests that more than one mechanism is responsible for the deviations. Substrate-induced rearrangement of liquid molecules in the close vicinity of the surface in the case of long-chain n-alkanes and adsorption of vapor onto the solid surface in the case of short-chain n-alkanes are the most likely explanations. The results suggest that liquids with bulky molecules appear to be suitable for contact angle measurements to characterize energetics of polymeric surfaces.     

Interpretation of contact angle measurements on two different fluoropolymers for the determination of solid surface tension

Contact angle measurements with a large number of liquids on the semi-fluorinated acryl polymer EGC-1700 films are reported. The surface tension was determined to be gammasv=13.84 mJ/m2 from contact angles of octamethylcyclotetrasiloxane (OMCTS) and decamethylcyclopentasiloxane (DMCPS). Inertness of these two liquids makes them ideal for determination of surface tension of low-energy fluoropolymers. On the other hand, contact angles of many other liquids deviated somewhat from a smooth contact angle pattern that represents the EGC-1700 surface tension. It is argued that noninertness of the molecules of these liquids gives rise to specific interactions with the polymer film, causing the deviations. Furthermore, contact angles of a series of n-alkanes (n-hexane to n-hexadecane) showed systematic deviations from this curve, similar to the trend observed for n-alkanes/Teflon AF 1600 systems studied earlier. Adsorption of vapor of short-chain liquids onto the polymer film caused their contact angles to fall above the gammasv=13.84 mJ/m2 curve, and a parallel alignment of molecules of the long-chain n-alkanes in the vicinity of the solid was the explanation for the deviation of their contact angles below it. It is found that vapor adsorption effect is more significant in the case of Teflon AF 1600, while the alignment of liquid molecules close to the surface is more pronounced for EGC-1700.     

Aggregation states and surface wettability in films of poly(styrene-block-2-perfluorooctyl ethyl acrylate) diblock copolymers synthesized by atom transfer radical polymerization

Well-defined poly(styrene-block-2-perfluorooctyl ethyl acrylate) [P(St-b-PFA)] copolymers with various chemical compositions were synthesized by atom transfer radical polymerization. Films of P(St-b-PFA) were structurally characterized, from bulk to surface, on the basis of transmittance electron microscopic observation and small-angle X-ray scattering, X-ray photoelectron spectroscopic, and contact angle measurements. For a comparison, poly(styrene-random-2-perfluorooctyl ethyl acrylate) [P(St-ran-PFA)] copolymers were also synthesized by conventional free radical polymerization. While P(St-b-PFA) with the 2-perfluorooctyl ethyl acrylate (PFA) content higher than 18.7 mol % formed a typical phase-separated cylinder structure, P(St-b-PFA) with a lower PFA content and P(St-ran-PFA) were in a miscible state. Since the perfluoroalkyl groups possess extremely low surface energy, they were preferentially segregated at the film surface, resulting in the formation of the PFA surface layer. This was the case for all P(St-b-PFA) films examined, although the aggregation state at the surface was strongly dependent on the PFA content. In the case of the P(St-b-PFA) with the PFA content higher than 18.7 mol %, both advancing and receding contact angles for water were 120 degrees and even larger with almost no hysteresis. In addition, extremely excellent oil-repellent surface properties such as advancing and receding contact angles for dodecane of 76 degrees and 75 degrees were also observed. However, these intriguing liquid-repellent properties were not observed for the films of miscible P(St-b-PFA) and P(St-ran-PFA). Therefore, it can be concluded that the internal structure beneath the surface as well as the surface itself should be deeply considered to design excellent and stable liquid-repellent materials.     

Surface heterogeneity and contact angle hysteresis

The effect of surface heterogeneity on contact angle hysteresis is studied by using the model of Neumann and Good of a vertical plate with horizontal heterogeneous strips. The results of this study explain well known, but not understood patterns of contact angle behaviour: On the one hand, the advancing contact angle on a carefully prepared solid surface is generally reproducible; on the other hand, even a very small amount of surface heterogeneity may cause the receding contact angle to be less reproducible and to depend on several non-thermodynamic factors.     

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.     

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.     

Wettability and topography of phospholipid DPPC multilayers deposited by spin-coating on glass, silicon, and mica slides

The surface free energy of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on glass, silicon, or mica by the spin-coating method was estimated. For this purpose, the advancing and receding contact angles of water, formamide, and diiodomethane were measured, and then two concepts of the interfacial interactions were applied. In the contact angle hysteresis approach, the apparent total surface free energy is calculated from the advancing and receding contact angles of the probe liquids, and in the Lifshitz-van der Waals/acid-base approach, the total surface free energy is calculated from previously determined components of the energy, that is, the apolar Lifshitz-van der Waals and the polar electron-donor and electron-acceptor, which are calculated from the advancing contact angles of the probe liquids alone. Comparison of the results obtained using these two approaches provided more information about changes in the hydrophobic/hydrophilic character of the DPPC layers and, simultaneously, a verification of the approaches. Moreover, the roughness and topography of the investigated layers were also examined by atomic force microscopy measurements. The hydrophilic character of the DPPC layers decreased if up to 0.5 mg of DPPC/mL was used to deposit on the substrates by the spin-coating method. Then it increased and leveled off if up to 2-2.5 mg of DPPC/mL was used. The changes in the energy were correlated with the changes in topography of the surfaces.     

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.